# Statistical Functions Part Three

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Financial Functions Part Three

## CUMIPMT

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

### Syntax

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

Rate is the periodic interest rate.

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

PV is the present cash value in sequence of payments.

S is the first period.

E is the last period.

Type (optional): the due date of the payment at the beginning or at the end of the period.

### Examples

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.

Calculates the accumulated interest for a period.

The functions whose names end with _ADD or _EXCEL2003 return the same results as the corresponding Microsoft Excel 2003 functions without the suffix. Use the functions without suffix to get results based on international standards.

### Syntax

Rate defines the interest rate per period.

NPer is 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.

StartPeriod is the first payment period for the calculation.

EndPeriod is the last payment period for the calculation.

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

### Examples

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)?

How much interest must you pay in the first month?

## CUMPRINC

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

### Syntax

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

Rate is the periodic interest rate.

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

PV is the present cash value in sequence of payments.

S is the first period.

E is the last period.

Type (optional): the due date of the payment at the beginning or at the end of the period.

### Examples

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.

Calculates the cumulative redemption of a loan in a period.

The functions whose names end with _ADD or _EXCEL2003 return the same results as the corresponding Microsoft Excel 2003 functions without the suffix. Use the functions without suffix to get results based on international standards.

### Syntax

Rate defines the interest rate per period.

NPer is 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.

StartPeriod is the first payment period for the calculation.

EndPeriod is the last payment period for the calculation.

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

### Examples

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)?

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

## DOLLARDE

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

### Syntax

DOLLARDE(Fractional dollar;Fraction)

FractionalDollar is a number given as a decimal fraction.

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

### Examples

=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.

## DOLLARFR

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

### Syntax

DOLLARFR (Decimal dollar;Fraction)

DecimalDollar is a decimal number.

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

### Examples

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

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

## DURATION

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

### Syntax

DURATION(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 is 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.

### Examples

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.

## MDURATION

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

### Syntax

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

Yield: the annual yield of the security.

Maturity: the date on which the security is sold.

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

Yield: the annual yield of the security.

P is the number of interest payment periods per year.

Basis: is chosen from a list of options and indicates how the year is to be calculated.

 Basis Calculation 0 or missing US method (NASD), 12 months of 30 days each 1 Exact number of days in months, exact number of days in year 2 Exact number of days in month, year has 360 days 3 Exact number of days in month, year has 365 days 4 European method, 12 months of 30 days each

### Examples

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.

## MIRR

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

### Syntax

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)

### Examples

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%.

## NOMINAL

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

### Syntax

EffectiveRate is the effective interest rate

NPERY: the number of periodic interest payments per year.

### Examples

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%.

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

The functions whose names end with _ADD or _EXCEL2003 return the same results as the corresponding Microsoft Excel 2003 functions without the suffix. Use the functions without suffix to get results based on international standards.

### Syntax

EffectiveRate is the effective annual rate of interest.

P is the number of interest payment periods per year.

### Examples

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

## 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.

### Syntax

NPV(Rate; Value1; Value2; ...; Value30)

Rate defines the interest rate per period.

Value1, Value2, ..., Value30 are up to 30 values, which represent deposits or withdrawals.

### Examples

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.

## PMT

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

### Syntax

PMT(Rate; NPER; PV; FV; Type)

Rate is the periodic interest rate.

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

PV is the present cash value in 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.

### Examples

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.

## 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.

### Syntax

PPMT(Rate;Period;NPER;PV;FV;Type)

Rate is the periodic interest rate.

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

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

PV is the present cash value in sequence of payments.

FV (optional) is 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.

### Examples

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.

## 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.

### Syntax

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

Yield: the annual yield of the security.

Maturity: the date on which the security is sold.

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

Yield: the annual yield of the security.

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

P is the number of interest payment periods per year.

Basis: is chosen from a list of options and indicates how the year is to be calculated.

 Basis Calculation 0 or missing US method (NASD), 12 months of 30 days each 1 Exact number of days in months, exact number of days in year 2 Exact number of days in month, year has 360 days 3 Exact number of days in month, year has 365 days 4 European method, 12 months of 30 days each

### Examples

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.

## PRICEDISC

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

### Syntax

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

Yield: the annual yield 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 of the security per 100 currency units of par value.

Basis: is chosen from a list of options and indicates how the year is to be calculated.

 Basis Calculation 0 or missing US method (NASD), 12 months of 30 days each 1 Exact number of days in months, exact number of days in year 2 Exact number of days in month, year has 360 days 3 Exact number of days in month, year has 365 days 4 European method, 12 months of 30 days each

### Examples

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.

## PRICEMAT

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

### Syntax

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

Yield: the annual yield of the security.

Maturity: the date on which the security is sold.

Yield: the annual yield of the security.

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

Yield: the annual yield of the security.

Basis: is chosen from a list of options and indicates how the year is to be calculated.

 Basis Calculation 0 or missing US method (NASD), 12 months of 30 days each 1 Exact number of days in months, exact number of days in year 2 Exact number of days in month, year has 360 days 3 Exact number of days in month, year has 365 days 4 European method, 12 months of 30 days each

### Examples

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.

## SLN

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

### Syntax

SLN(Cost; Salvage; Life)

Cost fixes the initial cost of an asset.

Salvage is the value of an asset at the end of the depreciation.

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

### Examples

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.

## 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.

### Syntax

TBILLEQ(Settlement;Maturity;Discount)

Yield: the annual yield of the security.

Maturity: the date on which the security is sold.

Discount: the percentage discount on acquisition of the security.

### Examples

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("3/31/99";"6/1/99"; 0.0914) returns 0.094151 or 9.4151 per cent.

## TBILLPRICE

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

### Syntax

TBILLPRICE(Settlement;Maturity;Discount)

Yield: the annual yield of the security.

Maturity: the date on which the security is sold.

Discount: the percentage discount on acquisition of the security.

### Examples

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.

## TBILLYIELD

Calculates the yield of a treasury bill.

### Syntax

TBILLYIELD(Settlement;Maturity;Price)

Yield: the annual yield 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.

### Examples

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("3/31/99";"6/1/99"; 98.45) returns 0.091417 or 9.1417 per cent.

## YIELD

Calculates the yield of a security.

### Syntax

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

Yield: the annual yield of the security.

Maturity: the date on which the security is sold.

Rate is the annual rate of interest.

Price: The price of the security per 100 currency units of par value.

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

P is the number of interest payment periods per year.

Basis: is chosen from a list of options and indicates how the year is to be calculated.

 Basis Calculation 0 or missing US method (NASD), 12 months of 30 days each 1 Exact number of days in months, exact number of days in year 2 Exact number of days in month, year has 360 days 3 Exact number of days in month, year has 365 days 4 European method, 12 months of 30 days each

### Examples

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("2/15/1999"; "11/15/2007"; 0.0575 ;95.04287; 100; 2; 0) returns 0.065 or 6.5 per cent.

## YIELDDISC

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

### Syntax

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

Yield: the annual yield of the security.

Maturity: the date on which the security is sold.

Price: The price of the security per 100 currency units of par value.

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

Basis: is chosen from a list of options and indicates how the year is to be calculated.

 Basis Calculation 0 or missing US method (NASD), 12 months of 30 days each 1 Exact number of days in months, exact number of days in year 2 Exact number of days in month, year has 360 days 3 Exact number of days in month, year has 365 days 4 European method, 12 months of 30 days each

### Examples

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("2/15/1999"; "3/1/1999"; 99.795; 100; 2) returns 0.052823 or 5.2823 per cent.

## YIELDMAT

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

### Syntax

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

Yield: the annual yield of the security.

Maturity: the date on which the security is sold.

Yield: the annual yield of the security.

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

Price: The price of the security per 100 currency units of par value.

Basis: is chosen from a list of options and indicates how the year is to be calculated.

 Basis Calculation 0 or missing US method (NASD), 12 months of 30 days each 1 Exact number of days in months, exact number of days in year 2 Exact number of days in month, year has 360 days 3 Exact number of days in month, year has 365 days 4 European method, 12 months of 30 days each

### Examples

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("3/15/1999"; "11/3/1999"; "11/8/1998"; 0.0625; 100.0123; 0) returns 0.060954 or 6.0954 per cent.

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Financial Functions Part Three