Question

Mohal is going to invest $830 and leave it in an account for 8 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Mohal to end up with $1,110?

Answer 1

3.63%

Explanation:

You want to know the interest rate compounded daily that will result in an $830 investment being worth $1110 in 8 years.

Compound interest

The value of the investment of P earning interest at rate r compounded n times per year for t years is ...

A = P(1 +r/n)^(nt)

Filling in the given values, we have ...

1110 = 830(1 +r/365)^(365·8)

Dividing by 830 and taking the 2920-th root gives ...

(1110/830)^(1/2920) = 1 +r/365

Then the value of the interst rate r is ...

r = 365·((111/83)^(1/2920) -1) ≈ 0.036338 ≈ 3.63%

Mohal's investment requires an interest rate of 3.63%.

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Additional comment

A financial calculator can solve this, too, as shown in the second attachment.

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