FM for Actuaries

Interest Accumulation and Time Value of Money 31
1.15 Find the present value of $500 to be paid at the end of 28 months.
(a) if the nominal interest rate is 6% convertible monthly,
(b) if the nominal discount rate is 6% compounded every 4 months,
(c) if the nominal interest rate is 4% compounded semiannually,
(d) if the nominal discount rate is 5% payable annually.
Apply the simple-interest method for the remaining fraction of the conversion
period if necessary.
1.16 When does the rule of 72 hold exactly?
1.17 You wish to borrow $10,000. The following is the information you gathered
from two lenders:
(a) Lender A charges 7% compounded quarterly,
(b) Lender B charges an annual effective rate of interest of 7.25%.
Which lender would you choose?
1.18 A Treasury Bill for $100 is purchased for $95 four months before due. Find
the nominal rate of discount convertible three times a year earned by the
purchaser.
1.19 You are given the following stream of cash flows:
t C t
0 950
1 800
2 150
3 400
4 120
Find the present value and the future value (after 5 years) of the cash flows
evaluated at i =2%.
1.20 (a) Extend formula (1.36) to the case when the interest rate is not constant
over time.