At the end of each year Mr. Smith deposits $6,000 into an investment fund. The f

Question

At the end of each year Mr. Smith deposits $6,000 into an investment fund. The fund pays out interest each year at an annual effective interest rate of 6%. Mr. Smith is only able to reinvest this interest at an annual effective interest rate of 4%. Assuming Mr. Smith continues to make his $6,000 deposits for twenty years, that he always immediately deposits all the interest paid out into the 4% account, and that makes no withdrawals, what’s the accumulated value of Mr. Smith’s investments at the time of the last deposit?

Explanation / Answer

The table of Investments, the interest payout at 6% and reinvetment of the interest at 4% is as shown below:

Year Investment at the end of the year Interest Paid at the end of the year Investment od payout at 4% interest 1 6000 0 0 2 12000 360 0 3 18000 720 374.4 4 24000 1080 1123.2 5 30000 1440 2246.4 6 36000 1800 3744 7 42000 2160 5616 8 48000 2520 7862.4 9 54000 2880 10483.2 10 60000 3240 13478.4 11 66000 3600 16848 12 72000 3960 20592 13 78000 4320 24710.4 14 84000 4680 29203.2 15 90000 5040 34070.4 16 96000 5400 39312 17 102000 5760 44928 18 108000 6120 50918.4 19 114000 6480 57283.2 20 120000 6840 64022.4

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