ReviewView T Normal! TNoSpac Heading 1 Heading ??iv-? L2.E. Paragraph HW Problem

Question

ReviewView T Normal! TNoSpac Heading 1 Heading ??iv-? L2.E. Paragraph HW Problems -Chapter 4 What is the present value of $1,500 due in 14 years at a (a) 5 percent interest rate and (b) 10 percent rate. Explain why the present val- 4-5 ue is lower when the interest rate is higher. What is the present value (PV) of an investment that will pay $2,500 in five years if the opportu- nity cost rate is 9 percent compounded (a) annu ally, (b) quarterly, and (c) monthly? Explain why the PV is lowest when interest is compounded 4-7 monthly 4-9 Suppose you invest $385 at the end of each of the next eight years. (a) If your opportunity cost is 7 percent compounded annually, how much will your investment be worth after the last $385 payment is made? (b) What will be the ending amount if the payments are made at the beginning of each year? 4-14 Rebecca would like to set up an account to supplement her parents' retirement income for the next 15 years. (a) If the account earns 7.2 percent compounded

Explanation / Answer

As per rules I will answer the first 4 subparts of the question.

4-5

1:PV= FV/(1+r)^n

= 1500/1.05^14 = 757.60

2:PV = 1500/1.1^14 =$395

PV is lower when rate is higher since we are discounting by the rate. Higher the rate higher the denominator and hence lower is the PV.

4-7

3: PV = FV/(1+r)^n

= 2500/1.09^5 = 1624.83

4: PV= 2500/(1+ 0.09/4)^(5*4)

=1602.04

5: PV= 2500/(1+ 0.09/12)^(5*12) = $1596.75

With less compounding a person has to deposit more to earn the same amount. As the compounding is higher, the investor can deposit lesser amount.

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