Question

An amount of 1000 is deposited into Fund X, which earns an effective annual interest rate of 6%. At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year, the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y, which earns an effective annual interest rate of 9%. Determine the accumulated value of Fund Y at the end of year 10.

Answer 1

Amount Deposited = $1000

Interest Earned = 6%

Amount withdrawn at end of Year 1 = 1000*6% + 100 = 160
Amount withdrawn at end of Year 2 = 900*6% + 100 = 154
Amount withdrawn at end of Year 3 = 800*6% + 100 = 148
Amount withdrawn at end of Year 4 = 700*6% + 100 = 142
Amount withdrawn at end of Year 5 = 600*6% + 100 = 136
Amount withdrawn at end of Year 6 = 500*6% + 100 = 130
Amount withdrawn at end of Year 7 = 400*6% + 100 = 124
Amount withdrawn at end of Year 8 = 300*6% + 100 = 118
Amount withdrawn at end of Year 9 = 200*6% + 100 = 112
Amount withdrawn at end of Year 10 = 100*6% + 100 = 106

The amounts are invested in a fund providing an interest rate of 9%

FV of an amount after n years = PV(1+r)ⁿ

FV of fund in account at end of Year 10 = 160(1+0.09)⁹ + 154(1+0.09)⁸ + 148(1+0.09)⁷ + 142(1+0.09)⁶ + 136(1+0.09)⁵ + 130(1+0.09)⁴ + 124(1+0.09)³ + 118(1+0.09)² + 112(1+0.09) + 106 = $2084.67