Question

Suppose you have an initial deposit of $4000 in a bank. After 2 years, you have a deposit amount of $4240. What was your annual interest rate? (For 9.99 percent enter 9.99 not 0.0999. If necessary, round to two decimal places for percentage value).

Suppose you have an initial deposit of $100 in a bank. After 10 years, you have a deposit amount of $260. What was your annual interest rate? (For 9.99 percent enter 9.99 not 0.0999. If necessary, round to two decimal places for percentage value).

Answer 1

Question 1

Initial deposit = $4000

Deposit after 2 years = $4240

Time period (n) = 2 years

Calculate the annual interest rate -

Annual interest rate = [(Deposit after 2 years/Initial deposit)^1/n] - 1

Annual interest rate = [(4240/4000)^1/2] - 1

Annual interest rate = [(1.06)^0.5] - 1

Annual interest rate = 1.0295 - 1

Annual interest rate = 0.0295 or 2.95%

Thus,

The annual interest rate is 2.95 percent.

Question 2

Initial deposit = $100

Deposit after 10 years = $260

Time period (n) = 10 years

Calculate the annual interest rate -

Annual interest rate = [(Deposit after 10 years/Initial deposit)^1/n] - 1

Annual interest rate = [(260/100)^1/10] - 1

Annual interest rate = [(2.60)^0.10] - 1

Annual interest rate = 1.1002 - 1

Annual interest rate = 0.1002 or 10.02%

Thus,

The annual interest rate is 10.02 percent.