Question

Adam invested $6139 in an account with a fixed annual interest rate compounded continuously. after 17 years the balance reached $8624.97, what is the interest rate of the account?

Answer 1

2%

Explanation:

You want to know the interest rate on an account that has a value of $8624.97 after 17 years of continuous compounding for an investment of $6139.

Value

The value of an account earning interest compounded continuously is ...

A = Pe^(rt)

where r is the interest rate, t is the number of years, and P is the amount invested.

Rate

Solving for r, we get

A/P = e^(rt)

ln(A/P) = rt

r = ln(A/P)/t = ln(8624.97/6139)/17 ≈ 0.0200 = 2%

The interest rate of the account is 2%.

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