Question

You deposit $2,500 at the end of the year ( 0) into an account that pays interest at a rate of 7% compounded annually. Two years after your deposit, the savings account interest rate changes to 12% nominal interest compounded monthly. Five years after your deposit, the savings account again changes its interest rate this time the interest rate becomes 8% nominal interest compounded quarterly Nine years after your deposit, the saving account changes its rate once more to 6% compounded annually a. How much money should be in the savings account 15 years after the initial deposit, assuming no further changes in the account's interest rate? b. What interest rate, compounded annually, is equivalent to the interest pattern of the saving account in Part (a) over the entire 15 year period? as should be in the savings account 15 years after the initial deposit. (Round to the nearest dollar) b. The interest rate equivalent to the interest pattern of the saving account in Part(a) over the entire 15 year period is per year. (Round to one decimal place)

Answer 1

Deposit amount = $2500

Interest rate at K0 to K1 = 7% compound annually

Interest rate at K2 to K4 = 12% compound monthly

Interest rate at K5 to K8 = 8% compound quarterly

Interest rate at K9 to K14 = 6% compound annually

a) Amount after the end of 2 years =2500 ( 1 + 0.07)^2 = 28622.5

Amount after the end of 5 years = 28622.5 (1 + 0.12)^3 = 40212.55

Amount after the end of 9 years = 40212.5 (1 + 0.08)^4 = 54708.66

Amount after the end of 15 years = 54708.66 (1 + 0.06)^6 = 77605.27

Thus amount after 15 years = 77605.27

b) Initial amount = 25000 which becomes 77605.25 after 15 years.

Thus interest rate compounded annually in 15 years = 77602.5 = 25000 (1 + r)^15

1 + r = 1.078

r = 0.078 which makes annual interest rate of 7.8%