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

Answer:

n = 22

Step-by-step explanation:

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

$P.V.=P(\frac{1-(1+r)^{-n}}{r})$

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

$8000=400(\frac{1-(1+0.01)^{-n}}{0.01})$

After rearranging we have

$\frac{8000\times 0.01}{400}=1-1.01^{-n}$

$20\times 0.01=1-1.01^{-n}$

$1.01^{-n}$ = 1 - 0.2

$1.01^{-n}$ = 0.8

Taking log on both sides

-n log 1.01 = log 0.8

$n=\frac{-log0.08}{log1.01}$ = 22.4257

Therefore, n = 22

So there are total 22 payments