Question

Peyton is going to invest $440 and leave it in an account for 5 years. Assuming the

interest is compounded annually, what interest rate, to the nearest tenth of a percent,
would be required in order for Peyton to end up with $520?

Answer 1

The required interest rate would be of 3.4% a year.

Explanation:

The amount of money earned in compound interest, after t years, is given by:

`P(t) = P(0)(1+r)^t`

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Peyton is going to invest $440 and leave it in an account for 5 years.

This means that
`P(0) = 440, t = 5`

So

`P(t) = P(0)(1+r)^t`

`P(t) = 440(1+r)^5`

What interest rate, to the nearest tenth of a percent, would be required in order for Peyton to end up with $520?

This is r for which P(t) = 520. So

`P(t) = 440(1+r)^5`

`(1+r)^5 = (520)/(440)`

`\sqrt[5]{(1+r)^5} = \sqrt[5]{(52)/(44)}`

`1 + r = ((52)/(44))^{(1)/(5)}`

`1 + r = 1.034`

Then

`r = 1.034 - 1 = 0.034`

The required interest rate would be of 3.4% a year.