Question

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 1

$658.54

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:

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

She needs to make quarterly payment of $658.54