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Problem 31.21 in Dr. Fin. FM book

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  • Problem 31.21 in Dr. Fin. FM book

    So I ran into this problem and thought I solved it but it's not the same as the answer key. Could someone help me out if you can.

    An investment account is established on which it is estimated that 8% can be earned over the next 20 years. If the interest each year is subject to income tax at a 25% tax rate, find the percentage reduction in the accumulated interest at the end of 20 years.

    So I did some work. The accumulation before tax is 1.08^20. And after tax is 1.06^20 (isn't it)? So I took (1.06^20 - 1.08^20) / (1.08^20) and I got -31.1915% but the book said -39.71%. I don't know what I did wrong. Help!

  • #2
    (1 + i)^n is the accumulated value which including the principal and the interest. Since the question asks for percentage reduction in the accumulated interest only, we need to minus one from the accumulated value.

    1.06^20 -1 = 2.20713547 and 1.08^20 -1 = 3.66095714
    [(1.06^20 -1) - (1.08^20 -1)]/ (1.06^20 -1) * 100% = -39.711518% which is exactly the number you are looking for.

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    • #3
      Thanks a lot BeanCounter. This is very helpful.

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