Question

You deposit $3,000 at the end of the year (k = 0) into an account that pays interest at a rate of 7% compounded annually. A year after your deposit, the savings account interest rate changes to 1 2% nominal interest compounded month y Five years after ur de o the savings account aga changes it interest rate this time e interest rate becomes 8% nominal interest compounded quarterly. Eight 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?

Answer 1

Deposit = 3000

Effective rate for 1st yr = 7%

Effective rate for next 4 years = (1+0.12/12)^12 - 1 = 0.126828 = 12.68%

Effective rate for next 3 yrs = (1+0.08/4)^4 - 1 = 0.082432 = 8.24%

Effective rate for next 7 yrs = 6%

FW of deposit = 3000 * (1+0.07) * (1+0.1268)^4 * (1+0.0824)^3 * (1+0.06)^7

= 3000 * (1.07) * (1.1268)^4 * (1.0824)^3 * (1.06)^7

= 9867.26

b.

F = 9867.26

P = 3000

t = 15 yrs

F = P *(1+i)^t

9867.26 = 3000 * (1+i)^15

(1+i)^15 = 9867.26 / 3000 = 3.289088

i = 3.289088 ^ (1/15) -1

i = 1.082609 - 1 = 0.082609

i = 8.26%