Question

1. Future values for various compounding frequencies Delia Martin has $10,000 that she can deposit in any of three savings accounts for a 3-year period. Bank A compounds interest on an annual basis, bank B compounds interest twice each year, and bank C compounds interest each quarter. All three banks have a stated annual interest rate of 4%.

   1. What amount would Ms. Martin have after 3 years, leaving all interest paid on deposit, in each bank?

   2. What effective annual rate (EAR) would she earn in each of the banks?

   3. On the basis of your findings in parts a and b, which bank should Ms. Martin deal with? Why?

   4. If a fourth bank (bank D), also with a 4% stated interest rate, compounds interest continuously, how much would Ms. Martin have after 3 years? Does this alternative change your recommendation in part c? Explain why or why not.

Answer 1

a)

Bank A:

Future value = Present value (1 + r)ⁿ

Future value = 10000 (1 + 0.04)³

Future value = 10000 * 1.124864

Future value = $11,248.64

Bank B:
Number of periods = 3 * 2 = 6

Rate = 4% / 2 = 2%

Future value = Present value (1 + r)ⁿ

Future value = 10000 (1 + 0.02)⁶

Future value = 10000 * 1.126162

Future value = $11,261.62

Bank C:
Number of periods = 3 * 4 = 12

Rate = 4% / 4 = 1%

Future value = Present value (1 + r)ⁿ

Future value = 10000 (1 + 0.01)¹²

Future value = 10000 * 1.126825

Future value = $11,268.25

b)

Bank A:

Effective rate of bank A = 4%

Bank B:

Effective rate = (1 + APR/n)ⁿ - 1

Effective rate = (1 + 0.04/2)² - 1

Effective rate = ( 1.02)² - 1

Effective rate = 0.0404 or 4.04%

Bank C:

Effective rate = (1 + APR/n)ⁿ - 1

Effective rate = (1 + 0.04/4)² - 1

Effective rate = ( 1.01)⁴ - 1

Effective rate = 0.0406 or 4.06%

c)

It should deal with bank C as it has the highest EAR and future value.

d)

Future value of bank D = Present value e^r*t

Future value of bank D = 10,000e^0.04*3

Future value of bank D = 10,000e^0.12

Future value of bank D = 10,000 * 1.127497

Future value of bank D = $11,274.97

Alternative will change and bank D will be considered as it has the highest future value. This shows that as the compounding frequency increases, future value of a deposit will also increase.