Carlene is saving her money to buy a $500 desk. She deposits $400 into an account with an annual interest rate of 6% compounded continuously. The equation 400e^0.06t=500

represents the situation, where t is the number of years the money needs to remain in the account. About how long must Carlene wait to have enough money to buy the desk? Use a calculator and round your answer to the nearest whole number.

Question

Ernest

Mathematics

21 January, 09:54

Carlene is saving her money to buy a $500 desk. She deposits $400 into an account with an annual interest rate of 6% compounded continuously. The equation 400e^0.06t=500

represents the situation, where t is the number of years the money needs to remain in the account. About how long must Carlene wait to have enough money to buy the desk? Use a calculator and round your answer to the nearest whole number.

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Answers (1)

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Guadalupe Galloway · Answer 1

We want to determine t from the equation

400e^ (0.06t) = 500

Divide each side by 400.

e^ (0.06t) = 1.25

Take natural log of each side.

0.06t = ln (1.25) = 0.2231

t = 3.719 yrs

Answer: 4 years (nearest whole number)