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Becky would like to be a millionaire in 40 years. How much would she need to invest quarterly in a sinking fund paying a 9% interest ratecompounded quarterly to accumulate $1,000,000 in 40 years?She needs to make quarterly payment of $(Round up to the nearest cent.)

Answer :

ANSWER:

$658.54

STEP-BY-STEP EXPLANATION:

We have the following:

r = rate per period

R = periodic payment

n = number of periods

A = future value (accumulated value)

In this case:

4 month is 1 quarterly

r = 9% yearly = 9/(4*100) = 0.0225 quarterly

n = 40 years = 40*4 = 160 quarterly

A = 1000000

using below formula, we get:

[tex]\begin{gathered} R=\frac{A\cdot r}{(1+r)^n-1} \\ \text{ replacing:} \\ R=\frac{1000000\cdot0.0225}{\mleft(1+0.0225\mright)^{160}-1} \\ R=658.54 \end{gathered}[/tex]

She needs to make quarterly payment of $658.54

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