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Annuity loan

An annuity loan is paid back in periodic payments, which covers both installment and interest. The payments may be made weekly, monthly, quarterly or annual.

Formulas for annuity loans

PV: Present value (the initial payout)

r: Interest rate per term

n: Number of terms (number of payments until the loan is repaid)

P: Payment (the amount paid every term)

Calculating the payment:

P=PV*frac{r}{1-(1+r)^{-n}}

Calculating the present value:

PV=frac{P*(1-(1+r)^{-n})}{r}

Calculating the number of terms:

n=-frac{log(1-frac{PV*r}{P})}{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 additions of interest. More about that further down.

Calculate payment, present value and number of terms of an annuity loan

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).

Present value (PV): 
Interest rate (r): 
Number of terms (n): 
Payment (P): 

If you do not have the rate per term of an annuity loan

Unfortunately it’s not possible to make a formula for the rate per term. The only way to determine it is by trying to substitute different rates into the formula until it’s satisfactory

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 adition of interest

Extended calculator of annuity loan

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

Present value (PV): 
Interest rate (r): 
Number of terms (n): 
Terms per interest accrual (N): 
Payment (P):