Answer to Question #189556 in Financial Math for ntombi mshango

Question

Tshepo wants to buy a big screen TV. She has five interest rates to choose from if she borrows the money from the bank. The cheapest option for she is

[1] 29% per year, compounded daily.

[2] 30% per year, compounded semi-annually.

[3] 28,5% per year, compounded weekly

[4] 29,5% per year, compounded every two months.

[5] 29% per year, compounded monthly.

Answer 1

$A=P(1+\frac{r}{n})^(nt)$

A=final amount

P=initial principal

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

lets assume p=2000 and t=5 years

[1] 29% per year, compounded daily.

$2000\times(1+\frac{0.29}{365})^{365\times 5}=8521.33$

[2] 30% per year, compounded semi-annually.

$2000\times(1+\frac{0.3}{2})^{2\times 5}=80091.12$

[3] 28,5% per year, compounded weekly

$2000\times(1+\frac{0.285}{52})^{52\times 5}=8283.42$

[4] 29,5% per year, compounded every two months.

$2000\times(1+\frac{0.295}{6})^{6\times 5}=8440.43$

[5] 29% per year, compounded monthly.

$2000\times(1+\frac{0.29}{12})^{12\times 5}=8380.473$

Hence option 2 (30% per year, compounded semi-annually.) is the cheapest.