Answer:
n = 22
Step-by-step explanation:
We will use the formula for the present value of an ordinary annuity :
[tex]P.V.=P(\frac{1-(1+r)^{-n}}{r})[/tex]
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
[tex]8000=400(\frac{1-(1+0.01)^{-n}}{0.01})[/tex]
After rearranging we have
[tex]\frac{8000\times 0.01}{400}=1-1.01^{-n}[/tex]
[tex]20\times 0.01=1-1.01^{-n}[/tex]
[tex]1.01^{-n}[/tex] = 1 - 0.2
[tex]1.01^{-n}[/tex] = 0.8
Taking log on both sides
-n log 1.01 = log 0.8
[tex]n=\frac{-log0.08}{log1.01}[/tex] = 22.4257
Therefore, n = 22
So there are total 22 payments
