Answer:
54.72 months
Step-by-step explanation:
Given:
Future value = R35,000
Annuity = R500
Interest = 11.32% per year
Interest per month, r = [tex]\frac{11.32}{12}[/tex] = 0.943% = 0.00943
Let 'n' be the total time in months taken
Now,
Future value of annuity is calculated using the formula as:
[tex]\textup{Future value}=\textup{Annuity}\times[\frac{(1+r)^n-1}{r}][/tex]
on substituting the respective values, we get
[tex]35000=500\times[\frac{(1+0.00943)^n-1}{0.00943}][/tex]
or
[tex]70=[\frac{(1.00943)^n-1}{0.00943}][/tex]
or
1.6601 = 1.00943ⁿ
taking log both sides, we get
log(1.6601) = n × log(1.00943)
or
0.22= n × 0.00402
or
n = 54.72 months
