Question

Suppose you are planning to deposit $3,000 in a bank account. You'd like your deposit to grow to $6,000 in 3 years. If interest in the account compounds weekly, what annual interest rate do you need? Answer in percentage form and round to two decimal places.

Answer 1

PV =$3000

FV=$6000

n=3 years=3*52 weeks=156 weeks

Hence FV=PV**1+r)^n

Or, 6000=3000*(1+r)^156

Or, 6000/3000=(1+r)^156

Or 2^(1/156)=1+r

Or, r=1.004453-1

Or r=0.004453 or 0.4453%

This is weekly effective interest rate.

Hence annual effective interest rate = 0.4453%*52=23.15%

Effective interest rate=(1+i/n)^n-1,

Hence 23.15%=(1+i/52)^52-1

Or, 0.2315+1=(1+i/52)^52

Or, 1.2315^(1/52)=1+i/52

Or, 1.0040=1+i/52

Or, 1.0040-1=i/52

Or, 0.0040=i/52

Or, i=0.0040*52

Or, i=0.20865 or 20.86%

Hence Annual interest rate is 20.86% compounded weekly.