Answer to Question #196941 in Financial Math for Beauty Magadlela

Question

If 15% per year, interest is compounded every two months, then the equivalent weekly compounded rate is

[1] 14,464%.

[2] 14,837%.

[3] 14,484%.

[4] 14,816%.

[5] none of the above.

Answer 1

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

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

Let's take an example where p=$2000 t=10years

$A=2000(1+\frac{0.15}{6})^{(6\times10)}$

$=2000(1+0.025)^{60}$

$=\$ 8799.58$

The rate will be

$8799.58=2000(1+\frac{r}{52})^{(52×10)}$

$\frac{8799.58}{2000}=(1+\frac{r}{52})^{(520)}$

$4.39979=(1+\frac{r}{52})^{520}$

R=14.837%

Hence option [2] 14,837%. Is correct.