Question

Mr. Moshokoa wants to start saving early for his son's tertiary studies one day. He wants to pay 350 weekly into his account that returns 8,5% interest per year. How many years will it take him to have R400000 in the account?

Answer 1

The question illustrated above is an annuity payment problem, where an equal amount of 350 is paid weekly into an account yeilding an annual rate of 8.5%.

The future value of annuity is given by


`FV= P(\left(1+ (r)/(t) \right)^(nt)-1)/(\left( (r)/(t)\right) )`
where: Fv = 400,000
P = 350
r = 8.5% = 0.085
t = 52 {i.e. 52 weeks are in 1 year}
n is the number of years it will take for him to have R400,000.

Thus, we have


`400,000=350 (\left(1+ (0.085)/(52)\right)^(52n)-1 )/(\left((0.085)/(52)\right)) \\ \\ 1142.8571= ((1+0.001635)^(52n)-1)/(0.001635) \\ \\ 1.8681= (1.001635)^(52n)-1 \\ \\ 2.8681=(1.001635)^(52n) \\ \\ \log{2.8681}=52n\log{1.001635}`

`52n= \frac{\log{2.8681}}{\log{1.001635}} =644.9608 \\ \\ n= (644.9608)/(52) =12.4`

Therefore, it will take 12 years and 5 months for the money in the account be R400,000.