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Savings Annuity

An annuity can be used for savings, like for instance a life insurance, when a series of periodic payments are made into an account. Besides the accumulation of capital, the benefit of this is the compound interest that arises, when the interest being added to the principal of the deposit also earns interest and so forth.

Assuming that the interest rate is constant until the expiration of the annuity, the formula below can be used to calculate what the value of a given amount of money will be at a specific date in the future.

Formulas

FV = Future value (the amount of money that the annuity is worth after n terms)

P = Payment (the amount of money paid per term)

r = Interest rate

n = Number of terms (number of payments)


Future value after a specific number of payments:
FV=P*frac{(1+r)^n-1}{r}

Payment per term:
P=frac{FV*r}{(1+r)^n-1}

The number of terms:
n=frac{log(frac{FV*r}{P}+1)}{log(1+r)}


Please note
The formulas above only apply if there is exactly one payment and one addition of interest per term. If that’s not the case, you must convert the rate, so that the number of terms is the same as the number of times the interest is added. More about that further down.

If the rate is annual and the payment is monthly

If the rate is pro anno (the interest is compounded every year), and the payments are monthly, you must convert the rate to a monthly rate as well, before you can use the formula for annuity loan. The conversion from annual to monthly rate is given by:


From annual to monthly rate:
r_{monthly}=(1+r_{annual})^{frac{1}{12}}-1

or in general:

r_{new}=(1+r)^{frac{1}{N}}-1
where N = number of terms per addition of interest

Savings annuity calculator

Please enter at least three values, one of which must be the interest rate. The rate is written as a decimal number (for example, 9 % is written as 0.09).

Payment (P): 
Interest rate (r): 
Number of terms (n): 
Future value (FV):