Question

Wants to have $24.000 in 15 months. About how much should she put into a 15-month CD that earns simple interest of 6.4% a year calculated quarterly in order to reach her goal?

Answer 1

Required investment: `$22,222,23`

Explanation:

A CD that pays quarterly simple interest at the rate of `6.4%` per annum,
will pay `(6.4%)/4=1.6%` per quarter.

`15` months is equivalent to `5` quarters (3 months per quarter)

The formula for
`A`: accumulated value,
`P`: initial principle,
`r`: simple interest rate per period, and
`t`: number of periods
is
`A=P(1+rt)`

In this case we know
`A = 24000`,
`r= 1.6%`, and
`t=5`

So we have
`24000 = P(1+1.6% xx5)`

`color(white)("XXX")=P(1+8%)`

`color(white)("XXX")=P(108/100)`

Re-arranging we get
`P=24000 xx 100/108`

`color(white)("XX")=22222,2bar2`

She will need to invest `$22,222.23` in order to reach the goal of `$24,000`