Question

An interest rate of 14.90% per year compounded every three months is equivalent to a weekly compounded compounded interest rate of

Answer 1

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

Let P = 1, t = 1

$A=1(1+\frac{0.1940}{4})^4\\A=1.1575340471$

Compounded every week

$365÷7\approx52 \space weeks\\n=52\\1.1575340471=(1+\frac{r}{52})^{52}$

$\sqrt[52]{1.1575349471}=(1+\frac{r}{52})\\52\times \sqrt[52]{1.1575349471}-52=r\\r=0.14649789$

equivalent interest rate compounded weekly

r=0.14649789