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 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.

Explanation:

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 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.

Formula for Compound Interest A = ((P*(1+i)^n)

Where

A     =       final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

500 = ((400*(1+0.06)^n)

500 = 400 *1.06)^n

Divide both sides by 400

1.25 = 1.06^n

n = log 1.06 x 1.25 = 0.0312

Converted to months = 0.0312 * 12 months = 11 days

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