Question

Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem. PV $8,000; i 0.01; PMT $400; n = ? (Round up to the nearest integer.) n=

Answer 1

n = 22

Explanation:

We will use the formula for the present value of an ordinary annuity :

`P.V.=P((1-(1+r)^(-n))/(r))`

where P = periodic payment

r = rate per period

n = number of periods

Given P = PMT = $400, P.V. = $8,000, i = 0.01, and we have to find n.

Now we put the values in the formula

`8000=400((1-(1+0.01)^(-n))/(0.01))`

After rearranging we have

`(8000* 0.01)/(400)=1-1.01^(-n)`

`20* 0.01=1-1.01^(-n)`

`1.01^(-n)` = 1 - 0.2

`1.01^(-n)` = 0.8

Taking log on both sides

-n log 1.01 = log 0.8

`n=(-log0.08)/(log1.01)` = 22.4257

Therefore, n = 22

So there are total 22 payments