Question

Jasica Parker would like to have $48,000 to buy a new car in 7 years. To accumulate $48,000 in 7 years, how much should she invest monthly in a sinking fund with

3% interest compounded monthly?
The monthly invested payment is $
(Do not round until the final answer. Then round up to the nearest cent.)

Answer 1

$38,918.25

Explanation:

The equation you want to use for this is
`A=P(1+(r)/(n))^(nt)`:

• A = final Amount
• P = Principal (invested) amount
• r = interest Rate (as a decimal)
• n = the Number of times compounded each year
• t = the Time in years

You need to find P, so set up your equation:

`48000=P(1+(.03)/(12))^(12*7)`

Use the Order of Operations to simplify
`(1+(.03)/(12))^(12*7)`:

`(1+(.03)/(12))^(12*7)=(1+.0025)^(84)=1.0025^(84)`

Now solve for P:

`48000=P(1.0025^(84))`

`P=(48000)/(1.0025^(84))` ≈ 38918.24151

You'll want to round UP instead of off, because you're trying to find out how much to invest in order to have $48,000 and not still need a penny or two.