Question

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate? Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of

return of 6%? Explain.

Answer 1

The simple interest rate is 5%.

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

Explanation:

This is a simple interest problem.

The simple interest formula is given by:

`E = P*I*t`

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

`T = E + P`

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?

We have that
`P = 4200, E = 630, t = 3`. We have to find I.

`E = P*I*t`

`630 = 4200*I*3`

`I = (630)/(4200*3)`

`I = 0.05`

The simple interest rate is 5%.

Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of return of 6%?

We have to find T when
`P = 4200, t = 4, I = 0.06`

So

`E = P*I*t`

`E = 4200*0.06*4`

`E = 1008`

`T = E + P = 4200 + 1008 = 5208`

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.