Question

For liquidity purposes, a client keeps $100,000 in a bank account. The bank quotes a stated annual interest rate of 7% pa. The bank’s service representative explains that the stated rate is the rate one would earn if one were to cash out rather than invest the interest payments. a. With quarterly compounding, how much will you client have in his account at the end of one year, assuming no additions or withdrawals? b. With monthly compounding, how much will he have in his account at the end of one year, assuming no additions or withdrawals? c. With continuous compounding, how much will he have in his account at the end of one year, assuming no additions or withdrawals?

Answer 1

a)

With quarterly compunding:

Rate = 0.07 / 4 = 0.0175 or 1.75%

Number of periods = 1 * 4 = 4

Future value = Present value (1 + r)ⁿ

Future value = 100,000 ( 1 + 0.0175)⁴

Future value = 100,000 * 1.071859

Future value = $107,185.903

b)

With monthly compunding:

Rate = 0.07 / 12 = 0.005833 or 0.5833%

Number of periods = 1 * 12 = 12

Future value = Present value (1 + r)ⁿ

Future value = 100,000 ( 1 + 0.005833)¹²

Future value = 100,000 * 1.07229

Future value = $107,229

c)

Continous compounding:

Future value = 100,000e^0.07

Future value = 100,000 * 1.072508

Future value = $107,250.82

answered by: anonymous