Question

Allison is going to invest $43000 and leave it in an account for 14 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Allison to end up with $75,000?

Answer 1

3.97%

Explanation:

You want to know the interest rate that, compounded daily for 14 years, will result in a $43,000 investment having a value of $75,000.

Interest rate

There is no formula for the interest rate given the parameters of the problem. However, there are numerous calculators, apps, and spreadsheets that can find it for you.

The screen display of one such calculator is attached. It shows ...

The interest rate required is about 3.97%.

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Additional comment

Another way to find the rate is to use a graphing calculator to solve the compound interest formula for the rate required to give the desired result. In the second attachment, we have cast the problem in a way that makes the x-intercept of the graph be the interest rate in %.

(Since there are several leap years in 14 years, we used 365.25 days per year for compounding. This only affects the value of the interest rate percentage in its 7th decimal place, so doesn't change the answer.)

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