Question

3) Ravi invests $10,000 in an investment account that pays 4% compounded semi- annually. Ravi takes each interest payment and invests it in a savings account that pays 1% compounded monthly. a) How much money does Ravi have at the end of 10 years? b) What is the effective annual rate he earned over 10 years?

Answer 1

Answer a

Interest rate per period=4%/2=2%

Interest earned each period=2%*10000=$200

Hence each deposit will be $200 every 6 month

Effective rate for 1% compounded monthly=(1+1%/12)^12-1=(1+0.0833%)^12-1=1.000833^12-1=1.010046-1=0.010046 or 1.0046%

Semi annual rate=1.0046%/2=0.5023%

Hence the value in saving account will be future value of annuity of $200 at 0.5023% for 10*2=20 periods

Hence FV=A*((1+r)^n-1)/r

=200*((1+0.5023%)^20-1)/0.5023%

=200*(1.005023^20-1)/0.005023

=200*(1.1054-1))0.005023

=200*0.1054/0.005023

=4196.75

Hence total amount=10000+4196.75=$14196.75

Answer b

Fv=PV*(1+r)^n

Where r is effective annual rate

Hence 14196.75=10000*(1+r)^10

Or, 14196.75/10000=(1+r)^10

Or, 1.4197^(1/10)=1+r

Or, 1.0357=1+r

Or, r=1.0357-1

Or, r=0.0357 or 3.57%