Question

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

Answer 1

Answer:

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

Step-by-step 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

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

$(1+r)^5 = \frac{520}{440}$

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

$1 + r = (\frac{52}{44})^{\frac{1}{5}}$

$1 + r = 1.034$

Then

$r = 1.034 - 1 = 0.034$

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