You deposit $3000 every 6-months into a fund earning interest at j₂ = 7%.Immediately after the 9^th deposit,the interest rate changes to j₂ = 6%.How much is in your fund immediately after the 20^th deposit?

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity with changing interest rates:
FV = PMT * [(1+r1)^n1-1]/r1 + PMT * [(1+r1)^n1-1]/r1 * (1+r2)^n2 + PMT * [(1+r1)^n1-1]/r1 * (1+r2)^n2 * (1+r3)^n3 + ... + PMT * [(1+r1)^n1-1]/r1 * (1+r2)^n2 * (1+r3)^n3 * ... * (1+rn-1)^n(n-1) * (1+rn)^tn

Where PMT = $3000, r1 = 7%, n1 = 9 (number of compounding periods at 7%), r2 = 6%, n2 = 11 (number of compounding periods at 6%, starting from the 10th deposit), and tn = 40 (number of compounding periods at 6% after the 20th deposit).

Plugging in the values:

FV = $3000 * [(1+0.07)^9-1]/0.07 + $3000 * [(1+0.07)^9-1]/0.07 * (1+0.06)^11 + $3000 * [(1+0.07)^9-1]/0.07 * (1+0.06)^11 * (1+0.06)^40
FV = $38,433.49 + $30,765.98 + $12,281.19
FV = $81,480.66

Therefore, the answer is (C) $81,480.66.

You Deposit $3000 Every 6-Months into a Fund Earning Interest