Question

An interest rate of 14.92% per year compounded every three months is equivalent to a weekly compounded interest rate of

1.15.96%

2. 14.5%

3. 14.88%

4. 19.02%

Answer 1

If compounded every three months: $R=P(1+{\frac {0.1492} 4})^4=P*1.0373^4$ , where R - amount after 1 year, P - initial amount

If compounded every week: $R=P(1+{\frac i {52}})^{52}$ , where R - amount after 1 year, P - initial amount

So, $P(1+{\frac i {52}})^{52}=P*1.0373^4\implies (1+{\frac i {52}})^{52}=1.0373^4\implies 1+{\frac i {52}}=1.0373^{{\frac 1 {13}}}\implies 1+{\frac i {52}}=1.00282\implies i=0.14664$

14.67%