Question

) What is the EAR corresponding to a nominal rate of 8% compounded semiannually? Compounded quarterly? Compounded daily?

b) Your client is 40 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $5,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 9% in the future. If she follows your advice, how much money will she have at 65?

c) You have $60,000 to put as a down payment on a new house that costs $480,000, and you have been quoted the following terms: 2.99% Annual Percentage Rate (APR), for 30 years. If you decide to purchase this home, what will your monthly payment be? Additionally, over the life of the loan what would your total interest expense be?

d) An investment will pay $ 1, 500 at the end of each year for 20 years, and on the date of the last payment will also make a separate payment of $40,000. If your required rate of return on this investment is 4%, how much would you be willing to pay for the investment today?

e) A client has $300,000 in an account that earns 8% per year, compounded monthly. The client's 35th birthday was yesterday and she will retire when the account value is $1 million. At what age can she retire if she puts no more money in the account? At what age can she retire if she puts $250 per month into the account every month, beginning one month from today?

Answer 1

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = {(1 + Rate/ Compounding period)^Compounding period} – 1

         = {(1 + 0.08/2)^2} – 1

         = {(1 + 0.04)^2} – 1

         = 1.0816 – 1

         = 8.16%

Hence, the EAR is 8.16%.

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = {(1 + Rate/ Compounding period)^Compounding period} – 1

         = {(1 + 0.08/4)^4} – 1

         = {(1 + 0.02)^4} – 1

         = 1.08243216 – 1

         = 8.243216%

Hence, the EAR is 8.243216%.

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = {(1 + Rate/ Compounding period)^Compounding period} – 1

         = {(1 + 0.08/365)^365} – 1

         = {(1 + 0.00021917808)^365} – 1

         = 1.08327757093 – 1

         = 8.327757093%

Hence, the EAR is 8.327757093%.