Question

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

1) 29% per year, compounded daily

2) 30% per year, compounded semi-annually

3) 28.5% per year, compounded weekly or

4) 29.5% per year, compounded every two months

Answer 1

We will assume Tshepo borrows $400 from the bank for a time period(t) of 1 year

$A\ =P\left(1\ +\ \frac{r}{n}\right)^{n*t}$

$A\ =400\left(1\ +\ \frac{0.29}{365}\right)^{365*1} = \$534.51$

$A\ =400\left(1\ +\ \frac{0.3}{2}\right)^{2*1} = \$529$

$A\ =400\left(1\ +\ \frac{0.285}{52}\right)^{52*1} = \$531.49$

$A\ =400\left(1\ +\ \frac{0.295}{6}\right)^{6*1} = \$533.49$

The cheapest for Tshepo will be when the rate is at 30% per year, compounded semi-annually.