Question

# A man deposits ​\$16,000 at the beginning of each year for 18 years in an account...

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

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

Feel free to ask in case of any query relating to this question

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