Is I the annual interest or monthly interest?
It will be assumed monthly interest.
Present Value, P = 13000
Payment (monthly) A = 550
interest (monthly) i = 0.015
The amortization formula would equate future value with the sum of all the payments, all increased at rate of interest i.
Future value = sum of all payments
Let R=1+i
PRn = A + AR + AR² + AR³ + ... + ARn-1
=A(Rn+1)/(R-1) (by factoring)
Hence
(Rn-1)/((R-1)*Rn) = P/A
To solve for the period n, there is no explicit formula to calculate.
The easiest way is to calculate the payment for a given period n.
If the payment matches 550, then the estimated n is correct.
For example,
The equation can be converted into a formula for the monthly payment, A
A=P(R-1)R^n/(R^n-1)
For
P=13000
R=1.015
we make a first estimate from
13000/550=23.6
We know n>23.6, so try 30
A=13000(.015)1.015^30/(1.015^30-1)
=541.3 < 550
So we try 29 payments
A=556.1
We then know that the period n lies between 29 and 30, and for all practical purposes, we would put it at 30.
using the formula for present value of ordinary annuity or the amortization formula to solve this problem.
PV=13000
I= .015
PMT=550
n?
2 answers
The right-hand side of the amortization formula should read:
A(Rn-1)/(R-1) (by factoring)
A(Rn-1)/(R-1) (by factoring)
2 answers