Sarah invested 53,000 in an account paying an interest rate of 4.5% compounded daily. 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 77,700?

Solution

Sarah invested 53, 000 in an account paying an interest rate of 4.5% compounded daily. 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 77, 700?

Solution

Time : 8.5

Solution steps

Translate the problem into an equation:

77700 = 53000 (1 + \frac{0.045}{365})^{365 t}

Solve for

t, 77700 = 53000 (1 + \frac{0.045}{365})^{365 t} : t = 8.5

Time : 8.5

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