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

Answer:

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.

Step-by-step 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.

$E = P*I*t$

$630 = 4200*I*3$

$I = \frac{630}{4200*3}$

$I = 0.05$

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.