# Financial Functions Part Two

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\<bookmark_value\>CUMPRINC_ADD function\</bookmark_value\>## CUMPRINC_ADD

Calculates the cumulative redemption of a loan in a period.

CUMPRINC_ADD(Rate;NPER;PV;Start period;End period;Type)

Rate: the interest rate for each period.

NPER: the total number of payment periods. The rate and NPER must refer to the same unit, and thus both be calculated annually or monthly.

PV is the current value.

Start period: the first payment period for the calculation.

End period: the last payment period for the calculation.

Type: the maturity of a payment at the end of each period (Type = 0) or at the start of the period (Type = 1).

The following mortgage loan is taken out on a house:

Rate: 9.00 per cent per annum (9% / 12 = 0.0075), Duration: 30 years (payment periods = 30 * 12 = 360), NPV: 125000 currency units.

How much will you repay in the second year of the mortgage (thus from periods 13 to 24)?

CUMPRINC_ADD(0.0075;360;125000;13;24;0) returns -934.1071

In the first month you will be repaying the following amount:

CUMPRINC_ADD(0.0075;360;125000;1;1;0) returns -68.27827

\<bookmark_value\>CUMIPMT_ADD function\</bookmark_value\>## CUMIPMT_ADD

Calculates the accumulated interest for a period.

CUMIPMT_ADD(Rate;NPER;Pv;Start period;End period;Type)

Rate: the interest rate for each period.

NPER: the total number of payment periods. The rate and NPER must refer to the same unit, and thus both be calculated annually or monthly.

PV is the current value.

Start period: the first payment period for the calculation.

End period: the last payment period for the calculation.

Type: the maturity of a payment at the end of each period (Type = 0) or at the start of the period (Type = 1).

The following mortgage loan is taken out on a house:

Rate: 9.00 per cent per annum (9% / 12 = 0.0075), Duration: 30 years (NPER = 30 * 12 = 360), Pv: 125000 currency units.

How much interest must you pay in the second year of the mortgage (thus from periods 13 to 24)?

=CUMIPMT_ADD(0.0075;360;125000;13;24;0) returns -11135.23.

How much interest must you pay in the first month?

=CUMIPMT_ADD(0.0075;360;125000;1;1;0) returns -937.50.

\<bookmark_value\>NOMINAL_ADD function\</bookmark_value\>## NOMINAL_ADD

Calculates the annual nominal rate of interest on the basis of the effective rate and the number of interest payments per annum.

NOMINAL_ADD(Effective rate;Npery)

Effective rate: the effective annual rate of interest.

Npery: the number of interest payments per year.

What is the nominal rate of interest for a 5.3543% effective rate of interest and quarterly payment.

=NOMINAL_ADD(5.3543%; 4) returns 0.0525 or 5.25%.

\<bookmark_value\>TBILLEQ function\</bookmark_value\>\<bookmark_value\>treasury bills;annual return\</bookmark_value\>\<bookmark_value\>annual return on treasury bills\</bookmark_value\>## TBILLEQ

Calculates the annual return on a treasury bill. A treasury bill is purchased on the settlement date and sold at the full par value on the maturity date, that must fall within the same year. A discount is deducted from the purchase price.

TBILLEQ(Settlement;Maturity;Discount)

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Discount: the percentage discount upon acquisition of the security.

Settlement date: March 31 1999, maturity date: June 1 1999, discount: 9.14 per cent.

The return on the treasury bill corresponding to a security is worked out as follows:

=TBILLEQ("1999-03-31";"1999-06-01"; 0.0914) returns 0.094151 or 9.4151 per cent.

\<bookmark_value\>YIELDDISC function\</bookmark_value\>\<bookmark_value\>rates of return;non-interest-bearing securities\</bookmark_value\>## YIELDDISC

Calculates the annual yield of a non-interest-bearing security.

YIELDDISC(Settlement; Maturity; Price; Redemption [; Basis])

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Price: the price (purchase price) of the security per 100 currency units of par value.

Redemption: the redemption value per 100 currency units of par value.

A non-interest-bearing security is purchased on 2/15/1999. It matures on 3/1/1999. The price is 99.795 currency units per 100 units of par value, the redemption value is 100 units. The basis is 2. How high is the yield?

=YIELDDISC("1999-02-15"; "1999-03-01"; 99.795; 100; 2) returns 0.052823 or 5.2823 per cent.

\<bookmark_value\>YIELDMAT function\</bookmark_value\>\<bookmark_value\>rates of return;securities with interest paid on maturity\</bookmark_value\>## YIELDMAT

Calculates the annual yield of a security, the interest of which is paid on the date of maturity.

YIELDMAT(Settlement; Maturity; Issue; Rate; Price [; Basis])

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Issue: the date of issue of the security.

Rate: the interest rate of the security on the issue date.

Price: the price (purchase price) of the security per 100 currency units of par value.

A security is purchased on 3/15/1999. It matures on 11/3/1999. The issue date was 11/8/1998. The rate of interest is 6.25%, the price is 100.0123 units. The basis is 0. How high is the yield?

=YIELDMAT("1999-03-15"; "1999-11-03"; "1998-11-08"; 0.0625; 100.0123; 0) returns 0.060954 or 6.0954 per cent.

\<bookmark_value\>calculating; accumulated interests\</bookmark_value\>\<bookmark_value\>accumulated interests\</bookmark_value\>\<bookmark_value\>CUMIPMT function\</bookmark_value\>## CUMIPMT

Calculates the cumulative interest payments, that is, the total interest, for an investment based on a constant interest rate.

CUMIPMT(Rate;NPER;pv;S;E;Type)

\<emph\>Rate\</emph\> sets the periodic interest rate.

NPER: the payment period with the total number of periods. NPER can also be a non-integer value.

PV. the present value in the sequence of payments.

S: the first period.

E: the last period.

Type: the due date of the payment at the beginning or end of each period.

What are the interest payments at a yearly interest rate of 5.5 %, a payment period of monthly payments for 2 years and a current cash value of 5,000 currency units? The start period is the 4th and the end period is the 6th period. The payment is due at the beginning of each period.

CUMIPMT(5.5%/12;24;5000;4;6;1) = -57.54 currency units. The interest payments for between the 4th and 6th period are 57.54 currency units.

\<bookmark_value\>PRICE function\</bookmark_value\>\<bookmark_value\>prices; fixed interest securities\</bookmark_value\>\<bookmark_value\>sales values;fixed interest securities\</bookmark_value\>## PRICE

Calculates the market value of a fixed interest security with a par value of 100 currency units as a function of the forecast yield.

PRICE(Settlement; Maturity; Rate; Yield; Redemption; Frequency [; Basis])

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

\<emph\>Rate\</emph\>: the annual nominal rate of interest (coupon interest rate).

\<emph\>Par\</emph\>: the par value of the security.

Redemption: the redemption value per 100 currency units of par value.

Frequency: number of interest payments per year (1, 2 or 4).

A security is purchased on 2/15/1999; the maturity date is 11/15/2007. The nominal rate of interest is 5.75%. The yield is 6.5%. The redemption value is 100 currency units. Interest is paid half-yearly (frequency is 2). With calculation on basis 0 the price is as follows:

=PRICE("1999-02-15"; "2007-11-15"; 0.0575; 0.065; 100; 2; 0) returns 95.04287.

\<bookmark_value\>MDURATION function\</bookmark_value\>\<bookmark_value\>Macauley duration\</bookmark_value\>## MDURATION

Calculates the modified Macauley duration of a fixed interest security in years.

MDURATION(Settlement; Maturity; Coupon; Yield; Frequency [; Basis])

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Coupon: the annual nominal rate of interest (coupon interest rate)

\<emph\>Par\</emph\>: the par value of the security.

Frequency: number of interest payments per year (1, 2 or 4).

A security is purchased on 1/1/2001; the maturity date is 1/1/2006. The nominal rate of interest is 8%. The yield is 9.0%. Interest is paid half-yearly (frequency is 2). Using daily balance interest calculation (basis 3) how long is the modified duration?

=MDURATION("2001-01-01"; "2006-01-01"; 0.08; 0.09; 2; 3) returns 4.02 years.

\<bookmark_value\>calculating;modified internal rates of return\</bookmark_value\>\<bookmark_value\>modified internal rates of return\</bookmark_value\>\<bookmark_value\>MIRR function\</bookmark_value\>\<bookmark_value\>internal rates of return;modified\</bookmark_value\>## MIRR

Calculates the modified internal rate of return of a series of investments.

MIRR(Values; investment; reinvest_rate)

Values:corresponds to the array or the cell reference for cells whose content corresponds to the payments.

investment:the rate of interest of the investments (the negative values of the array)

reinvest_rate:the rate of interest of the reinvestment (the positive values of the array)

Assuming a cell content of A1=-5, A2=10, A3=15, and A4=8, and an investment value of 0.5 and a reinvestment value of 0.1, the result is 94.16%.

## PDURATION

Calculates the number of periods required by an investment to attain the desired value.

PDURATION(Rate; PV; FV)

Rate: a constant. The interest rate is to be calculated for the entire duration (duration period). The interest rate per period is calculated by dividing the interest rate by the calculated duration. The internal rate for an annuity is to be entered as Rate/12.

PV: the present (current) value. The cash value is the deposit of cash or the current cash value of an allowance in kind. As a deposit value a positive value must be entered; the deposit must not be 0 or <0.

FV: the expected value. The future value determines the desired (future) value of the deposit.

At an interest rate of 4.75%, a cash value of 25,000 currency units and a future value of 1,000,000 currency units, a duration of 79.49 payment periods is returned. The periodic payment is the resulting quotient from the future value and the duration, in this case 1,000,000/79.49=12,850.20.

\<bookmark_value\>TBILLPRICE function\</bookmark_value\>\<bookmark_value\>treasury bills;prices\</bookmark_value\>\<bookmark_value\>prices;treasury bills\</bookmark_value\>## TBILLPRICE

Calculates the price of a treasury bill per 100 currency units.

TBILLPRICE(Settlement;Maturity;Discount)

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Discount: the percentage discount upon acquisition of the security.

Settlement date: March 31 1999, maturity date: June 1 1999, discount: 9 per cent.

The price of the treasury bill is worked out as follows:

=TBILLPRICE("1999-03-31";"1999-06-01"; 0.09) returns 98.45.

\<bookmark_value\>PRICEDISC function\</bookmark_value\>\<bookmark_value\>prices;non-interest-bearing securities\</bookmark_value\>\<bookmark_value\>sales values;non-interest-bearing securities\</bookmark_value\>## PRICEDISC

Calculates the price per 100 currency units of par value of a non-interest- bearing security.

PRICEDISC(Settlement; Maturity; Discount; Redemption [; Basis])

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Discount: the discount of a security as a percentage.

Redemption: the redemption value per 100 currency units of par value.

A security is purchased on 2/15/1999; the maturity date is 3/1/1999. Discount in per cent is 5.25%. The redemption value is 100. When calculating on basis 2 the price discount is as follows:

=PRICEDISC("1999-02-15"; "1999-03-01"; 0.0525; 100; 2) returns 99.79583.

\<bookmark_value\>PRICEMAT function\</bookmark_value\>\<bookmark_value\>prices;interest-bearing securities\</bookmark_value\>## PRICEMAT

Calculates the price per 100 currency units of par value of a security, that pays interest on the maturity date.

PRICEMAT(Settlement; Maturity; Issue; Rate; Yield [; Basis])

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Issue: the date of issue of the security.

Rate: the interest rate of the security on the issue date.

\<emph\>Par\</emph\>: the par value of the security.

Settlement date: February 15 1999, maturity date: April 13 1999, issue date: November 11 1998. Interest rate: 6.1 per cent, yield: 6.1 per cent, basis: 30/360 = 0.

The price is calculated as follows:

=PRICEMAT("1999-02-15";"1999-04-13";"1998-11-11"; 0.061; 0.061;0) returns 99.98449888.

\<bookmark_value\>calculating;nominal interest rates\</bookmark_value\>\<bookmark_value\>nominal interest rates\</bookmark_value\>\<bookmark_value\>NOMINAL function\</bookmark_value\>## NOMINAL

Calculates the yearly nominal interest rate, given the effective rate and the number of compounding periods per year.

NOMINAL(EFFECT_RATE;NPERY)

EFFECT_RATE: the effective interest rate

NPERY: the number of periodic interest payments per year.

What is the nominal interest per year for an effective interest rate of 13.5% if twelve payments are made per year.

NOMINAL(13.5%;12) = 12.73%. The nominal interest rate per year is 12.73%.

\<bookmark_value\>YIELD function\</bookmark_value\>\<bookmark_value\>rates of return;securities\</bookmark_value\>\<bookmark_value\>yields, see also rates of return\</bookmark_value\>## YIELD

Calculates the yield of a security.

YIELD(Settlement; Maturity; Rate; Price; Redemption; Frequency [; Basis])

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Rate: the annual rate of interest.

Price: the price (purchase price) of the security per 100 currency units of par value.

Redemption: the redemption value per 100 currency units of par value.

Frequency: number of interest payments per year (1, 2 or 4).

A security is purchased on 2/15/1999. It matures on 11/15/2007. The rate of interest is 5.75%. The price is 95.04287 currency units per 100 units of par value, the redemption value is 100 units. Interest is paid half-yearly (frequency = 2) and the basis is 0. How high is the yield?

=YIELD("1999-02-15"; "2007-11-15"; 0.0575 ;95.04287; 100; 2; 0) returns 0.065 or 6.50 per cent.

\<bookmark_value\>TBILLYIELD function\</bookmark_value\>\<bookmark_value\>treasury bills;rates of return\</bookmark_value\>\<bookmark_value\>rates of return of treasury bills\</bookmark_value\>## TBILLYIELD

Calculates the yield of a treasury bill.

TBILLYIELD(Settlement;Maturity;Price)

Issue: the date of issue of the security.

Maturity: the date on which the security is sold.

Price: the price (purchase price) of the treasury bill per 100 currency units of par value.

Settlement date: March 31 1999, maturity date: June 1 1999, price: 98.45 currency units.

The yield of the treasury bill is worked out as follows:

=TBILLYIELD("1999-03-31";"1999-06-01"; 98.45) returns 0.091417 or 9.1417 per cent.

\<bookmark_value\>fractions; converting\</bookmark_value\>\<bookmark_value\>converting;decimal fractions, into decimal numbers\</bookmark_value\>\<bookmark_value\>DOLLARDE function\</bookmark_value\>## DOLLARDE

Converts a quotation that has been given as a decimal fraction into a decimal number.

DOLLARDE(Fractional dollar;Fraction)

Fractional dollar: a number given as a decimal fraction.

Fraction: a whole number that is used as the denominator of the decimal fraction.

=DOLLARDE (1.02;16) stands for 1 and 2/16. This returns 1.125.

=DOLLARDE (1.1;8) stands for 1 and 1/8. This returns 1.125.

\<bookmark_value\>DOLLARFR function\</bookmark_value\>\<bookmark_value\>converting;decimal fractions, into mixed decimal fractions\</bookmark_value\>## DOLLARFR

Converts a quotation that has been given as a decimal number into a mixed decimal fraction.

DOLLARFR (Decimal dollar;Fraction)

Decimal dollar: a decimal number.

Fraction: a whole number that is used as the denominator of the decimal fraction.

=DOLLARFR(1.125;16) converts into sixteenths. The result is 1.02 for 1 plus 2/16.

=DOLLARFR(1.125;8) converts into eighths. The result is 1.1 for 1 plus 1/8.

\<bookmark_value\>PPMT function\</bookmark_value\>## PPMT

Returns for a given period the payment on the principal for an investment that is based on periodic and constant payments and a constant interest rate.

PPMT(Rate; Period; NPer; PV [ ; FV [ ; Type ] ])

\<emph\>Rate\</emph\> sets the periodic interest rate.

Period: the amortizement period. P=1 for the first and P=NPER for the last period.

NPER: the total number of periods during which annuity is paid.

PV. the present value in the sequence of payments.

FV (optional): the desired (future) value.

Type (optional): defines the due date. F=1 for payment at the beginning of a period and F=0 for payment at the end of a period.

In the LibreOffice Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.

How high is the periodic monthly payment at an annual interest rate of 8.75% over a period of 3 years? The cash value is 5,000 currency units and is always paid at the beginning of a period. The future value is 8,000 currency units.

PPMT(8.75%/12;1;36;5000;8000;1) = -350.99 currency units.

\<bookmark_value\>calculating; total amortizement rates\</bookmark_value\>\<bookmark_value\>total amortizement rates\</bookmark_value\>\<bookmark_value\>amortization installment\</bookmark_value\>\<bookmark_value\>repayment installment\</bookmark_value\>\<bookmark_value\>CUMPRINC function\</bookmark_value\>## CUMPRINC

Returns the cumulative interest paid for an investment period with a constant interest rate.

CUMPRINC(Rate;NPER;PV;S;E;Type)

\<emph\>Rate\</emph\> sets the periodic interest rate.

NPER: the payment period with the total number of periods. NPER can also be a non-integer value.

PV. the present value in the sequence of payments.

S: the first period.

E: the last period.

Type: the due date of the payment at the beginning or end of each period.

What are the payoff amounts if the yearly interest rate is 5.5% for 36 months? The cash value is 15,000 currency units. The payoff amount is calculated between the 10th and 18th period. The due date is at the end of the period.

CUMPRINC(5.5%/12;36;15000;10;18;0) = -3669.74 currency units. The payoff amount between the 10th and 18th period is 3669.74 currency units.

\<bookmark_value\>calculating;annuities\</bookmark_value\>\<bookmark_value\>annuities\</bookmark_value\>\<bookmark_value\>PMT function\</bookmark_value\>## PMT

Returns the periodic payment for an annuity with constant interest rates.

PMT(Rate; NPer; PV [ ; [ FV ] [ ; Type ] ])

\<emph\>Rate\</emph\> sets the periodic interest rate.

NPER: the number of periods in which annuity is paid.

PV: the present value (cash value) in a sequence of payments.

FV (optional): the desired value (future value) to be reached at the end of the periodic payments.

Type (optional): the due date for the periodic payments. Type=1 is payment at the beginning and Type=0 is payment at the end of each period.

In the LibreOffice Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.

What are the periodic payments at a yearly interest rate of 1.99% if the payment time is 3 years and the cash value is 25,000 currency units. There are 36 months as 36 payment periods, and the interest rate per payment period is 1.99%/12.

PMT(1.99%/12;36;25000) = -715.96 currency units. The periodic monthly payment is therefore 715.96 currency units.

\<bookmark_value\>calculating;net present values\</bookmark_value\>\<bookmark_value\>net present values\</bookmark_value\>\<bookmark_value\>NPV function\</bookmark_value\>## NPV

Returns the present value of an investment based on a series of periodic cash flows and a discount rate. To get the net present value, subtract the cost of the project (the initial cash flow at time zero) from the returned value.

If the payments take place at irregular intervals, use the XNPV function.

NPV(Rate; Number 1 [; Number 2 [; … [; Number 254]]])

RATE: the discount rate for a period.

What is the net present value of periodic payments of 10, 20 and 30 currency units with a discount rate of 8.75%. At time zero the costs were paid as -40 currency units.

NPV(8.75%;10;20;30) = 49.43 currency units. The net present value is the returned value minus the initial costs of 40 currency units, therefore 9.43 currency units.

\<bookmark_value\>calculating;linear depreciations\</bookmark_value\>\<bookmark_value\>depreciations;linear\</bookmark_value\>\<bookmark_value\>linear depreciations\</bookmark_value\>\<bookmark_value\>straight-line depreciations\</bookmark_value\>\<bookmark_value\>SLN function\</bookmark_value\>## SLN

Returns the straight-line depreciation of an asset for one period. The amount of the depreciation is constant during the depreciation period.

SLN(COST; SALVAGE; LIFE)

\<emph\>Cost\</emph\> fixes the initial cost of an asset.

\<emph\>Salvage\</emph\> is the value of an asset after depreciation.

LIFE: the depreciation period determining the number of periods in the depreciation of the asset.

Office equipment with an initial cost of 50,000 currency units is to be depreciated over 7 years. The value at the end of the depreciation is to be 3,500 currency units.

SLN(50000;3,500;84) = 553.57 currency units. The periodic monthly depreciation of the office equipment is 553.57 currency units.