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
[tex]FV= P\frac{\left(1+ \frac{r}{t} \right)^{nt}-1}{\left( \frac{r}{t}\right) } [/tex]
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
[tex]400,000=350 \frac{\left(1+ \frac{0.085}{52}\right)^{52n}-1 }{\left(\frac{0.085}{52}\right)} \\ \\ 1142.8571= \frac{(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}[/tex]
[tex]52n= \frac{\log{2.8681}}{\log{1.001635}} =644.9608 \\ \\ n= \frac{644.9608}{52} =12.4[/tex]
Therefore, it will take 12 years and 5 months for the money in the account be R400,000.
