Answer:
99.89 months or 8.32 years
Explanation:
This is an annuity problem. The formula is:
[tex]P=C[\frac{1-(1+r)^{-n}}{r}][/tex]
Where
P is the payment total need to be made
C is the periodic payment per period
r is the rate of interest
n is the time period
Given in the problem, you need to pay off 1032, so
P = 1032
Periodic payment of 20 per month, so
C = 20
Rate of interest 1.5% = 0.015, so
r = 0.015
Time (n) is what we want to find.
Substituting and using logs, we solve for t:
[tex]P=C[\frac{1-(1+r)^{-n}}{r}]\\1032=20[\frac{1-(1.015)^{-n}}{0.015}]\\51.6=[\frac{1-(1.015)^{-n}}{0.015}]\\0.774=1-(1.015)^{-n}\\1.015^{-n}=0.226\\\frac{1}{1.015^n}=0.226\\1.015^n=4.4248\\ln(1.015^n)=ln(4.4248)\\nln(1.015)=ln(4.4248)\\n=\frac{ln(4.4248)}{ln(1.015)}\\n=99.89[/tex]
It will require 99.89 months!
In years, that would be:
99.89/12 = 8.32 years!
