Jackson invested $320 in an account paying an interest rate of 3.2% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $410?

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Jackson invested $320 in an account paying an interest rate of 3.2% compounded continuously.

Assuming no deposits or withdrawals are made.

Then the number of years, for the value of the account to reach $410 will be

410 = 320 (1 + 0.032)ⁿ

1.28125 = (1.032)ⁿ

Taking log on both sides, then we have

log 1.28125 = n x log 1.032

n = 7.1159

n ≅ 8

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Jackson invested $320 in an account paying an interest rate of 3.2% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $410?​

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What is compound interest?

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Jackson invested $320 in an account paying an interest rate of 3.2% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $410?