# DURATION function

FUNCTIONS
Depreciation
Payment Streams, Annuities, Loans
Securities
Coupons
Miscellaneous

## DURATION

Returns the number of periods needed for an investment to reach a certain value.

### Syntax:

DURATION(rate; present_value; future_value)

rate: the interest rate per period that will apply to the investment.
present_value: the value of the investment now.
future_value: the desired value of the investment in the future.
DURATION returns an estimate of the number of periods required to turn present_value into future_value at a constant interest rate of rate, compounded each period.
It solves the equation:
present_value * (1 + rate)duration = future_value,
giving a result:
DURATION(rate; present_value; future_value) = LOG(future_value/present_value; 1 + rate).
The result is exact for whole periods, and approximate for partial periods.

### Example:

DURATION(10%; 100; 121)

returns 2. \$100 invested at a 10% compounded annual rate is worth \$110 next year and \$121 in two years time.

### Issues:

• Calc's DURATION function is implemented as G_DURATION in Gnumeric, and is not implemented in Excel.
• The DURATION function as implemented in Gnumeric and Excel (Macaulay duration) is implemented as DURATION_ADD in Calc.
• The inexactness for fractional periods arises because interest is calculated linearly during a period. For example, \$100 at 10% is worth \$105 in half a year, yet DURATION(10%; 100; 105) does not return exactly 0.5. This may be of more theoretical than practical importance.