Question

Moses invests R3 745,35 at the end of each month at an interest rate of 14,5% per year, compounded
monthly. How long will it take him to have R1 000 000,00? Give your answer to the nearest year.

Answer 1

Calculating the number of months required (n):

$FV\space of\space annuity=P\times[\frac{(1+r)^n-1}{r}]$

$1,000,000=3,745.35\times[(\frac{1+\frac{0.145}{12})^n-1}{\frac{0.145}{12}}]$

$\frac{1,000,000}{3,745.35}\times0.012083=(1.012083)^n-1$

$3.226223+1==(1.012083)^n$ ( now flip the equation and take log both sides)

$n\times log(1.012083)=log (4.226223)$

$n=\frac{log(4.226223)}{log(1.012083)}$

$n=119.99$

Where:

the future value of annuity = 1,000,000

the monthly payment (P) = 3,745.35

the monthly inteest rate $=\frac{0.145}{12}$

Thus, the given annuity will take 119.99 months, i.e., 120 months rounded off, or 10 years to achieve 1,000,000.00. 

10 years