Question

An advertisement of an investment firm states that if you invest $500 in their firm today you will get $1000 at the end of 4.5 years. What nominal rate is implied if interest is compounded (a) quarterly (b) monthly? determine also the effective rate of interest in each case .

Answer 1

Given

Initial Deposit D=$500

Future Value FV=$1000

Number of years =4.5 years=4 years 6 months

A) If Compounded Quarterly

Let r be the rate of quarterly interest rate

Number of periods N=4*4.5=18 quarters

So FV=D*(1+r)^N

1000=500*(1+r)^18

r=3.93%

Nominal Interest Rate =4*r=4*3.93%=15.70%

Effective interest rate =(1+r)^4-1=(1+3.93%)^4-1=16.65%

B) If Compounded monthly

Let r be the rate of monthly interest rate

Number of periods N=12*4.5= 54 months

So FV=D*(1+r)^N

1000=500*(1+r)^54

r=1.29%

Nominal Interest Rate =12*r=12*1.29%=15.50%

Effective interest rate =(1+r)^12-1=(1+1.29%)^12-1=16.65%