Question

Mrs. Smith makes provision for her own pension. She invests $240 every month starting 1 month after her 30th birthday, into an account that pays 9% per annum compounded monthly. How much will she have on her 50th birthday?

Answer 1

The amount is computed as shown below:

Future value = Monthly investment x [ [ (1 + r)ⁿ – 1 ] / r ]

r is computed as follows:

= 9% / 12 (Since the interest is compounded monthly, hence divided by 12)

= 0.75%

n is computed as follows:

= (50 - 30) x 12 (Since the interest is compounded monthly, hence multiplied by 12)

= 240

So, the amount is computed as follows:

= $ 240 x [ [ (1 + 0.0075)²⁴⁰ - 1 ] / 0.0075 ]

= $ 240 x 667.8868699

= $ 160,292.85 Approximately

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