Question

A man deposits ​$16,000 at the beginning of each year for 18 years in an account paying 6​% compounded annually. He then puts the total amount on deposit in another account paying 9​% compounded semiannually for another 13 years. Find the final amount on deposit after the entire 31​-year period.

He will have a final amount of $____? after the entire 31-year period

​(Simplify your answer. Round to the nearest cent as​ needed.)

Answer 1

The amount is computed as follows:

value till 18 years is computed as follows:

Future value = Annual deposits x [ [ (1 + r)ⁿ – 1 ] / r ] x (1 + r)

= $ 16,000 x [ [ (1 + 0.06)¹⁸ - 1 ] / 0.06 ] x 1.06

= $ 16,000 x 30.90565255 x 1.06

= $ 524,159.8672

So, the amount till 31 years will be as follows:

= $ 524,159.8672 x (1 + r / 2) ^{n x 2} (r is divided by 2 and n is multiplied by 2, since the interest is semi annually compounded)

= $ 524,159.8672 x (1 + 0.09 / 2)^{13 x 2}

= $ 524,159.8672 x 1.045²⁶

= $ 1,646,217.89 Approximately

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