The Mathematics of Money

A. Comparing Effective and Nominal Rates

1. An bank is offering to pay an interest rate of 6.3% compounded monthly. The APY is given as 6.49%. Find the future
   value of $3,560.75 in 2 years, using the nominal rate and then using the APY. Do your answers match? Should they?


2. A credit union is offering to pay an interest rate of 4.92% compounded daily. The APY is given as 5.04%. Find the
   present value required to produce $20,000 in 1 year, fi rst using the nominal rate, and then using the APY. Do your
   answers match? Should they?


3. Melina invested $4,000 for 7 years at a nominal rate of 5.43% compounded quarterly.

a. Find the effective interest rate which is equivalent to 5.43% compounded quarterly.

b. Find Melina’s future value using the nominal rate.

c. Find Melina’s future value using the effective rate.

d. Do your answers to (b) and (c) agree? Should they?

4. Bob deposited $17,345.92 at a nominal rate of 4^3 ⁄ 4 % compounded daily for 1 year.

a. Find the effective rate of interest.

b. Find the future value using the nominal rate.

c. Find the future value using the effective rate.

d. Do your answers to (b) and (c) agree? Should they?

5. Kelsey deposited $39,559.01 in a 5-year certifi cate of deposit paying 5.98% compounded monthly.

a. Find Kelsey’s future value using the nominal rate.

b. Find the effective interest rate.

c. Find the future value using the effective rate.

d. Your answers to (a) and (c) will not be the same. Which answer gives the actual value of her account at the end of

5 years?

6. Paolo borrowed $3,945 for 6 months at an interest rate of 12.99% compounded monthly.

a. Find the total interest he will pay using the nominal rate.

b. Find the effective interest rate.

c. Find the total interest he will pay using the effective rate.

d. Which is the actual amount of interest he will pay, (a) or (c)?

7. Meryl invested $2,500 for 2 years at 9.75% compounded daily.

a. Find the total interest he will earn using the nominal rate.

b. Find the effective rate, and use it to fi nd the total interest he will earn.

EXERCISES 3.4

130 Chapter 3 Compound Interest