The first section of the test addresses time value of money analysis. John and Mary are a young couple, who want to put their finance in order. Both the husband and the wife are 27 years ago and in stable employment. They want to manage their savings and earning to achieve a better return and reduce the risks. You want to help them in their financial planning by answering a series of questions as follows:
a.The great Albert Einstein once said “Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”
i.What is the future value of an initial $500 after 30 years if it is invested in an account paying 15 percent annual interest?
ii. What is the present value of $1000000 to be received in 15 years if the appropriate interest rate is 12 percent?

b.(i) What is the difference between an ordinary annuity and an annuity due?

(ii)What are the future value and present value of a five-year ordinary annuity of $1000 if the appropriate interest rate is 10 percent? What would the future and present values be if the annuity were an annuity due?
1.Present value of ordinary annuity
2.Future value of ordinary annuity

3.Future value of annuity due

4.Present value of ordinary annuity

c.Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every six months, or semiannually—holding the stated interest rate constant? Why?

What is the effective annual rate for a simple rate of 12 percent?
(i)Compounded semiannually?
(ii)Compounded quarterly?

(iii)Compounded daily?

d.Suppose someone offered to sell you a note that calls for a $1,000 payment 15 months from today. The person offers to sell the note for $850. You have $850 in a bank time deposit (savings instrument) that pays a 6.76649 percent simple rate with daily compounding, which is a 7 percent effective annual interest rate; and you plan to leave this money in the bank unless you buy the note. The note is not risky—that is, you are sure it will be paid on schedule. Should you buy the note? Check the decision in both ways: (1) by comparing your future value if you buy the note versus leaving your money in the bank, (2) by comparing the PV of the note with your current bank investment.