SOLUTION: Recall that the formula for compounding interest is A = P(1+ r)t where A is the total accumulated amount in an account with principal P compounded at a annual interest rate r once

Question 213724: Recall that the formula for compounding interest is A = P(1+ r)t where A is the total accumulated amount in an account with principal P compounded at a annual interest rate r once per year for t years.
a. How many years will it take for a principal of
P =1000 to reach an amount of A = 5000 when compounded once a year at an annual interest rate of 6%?
b. If the interest rate is doubled to 12%, what will the number of years be for the
principal of P =1000 to reach an amount of A = 5000?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

Start with the given equation.

Plug in , , and

Add

Divide both sides by 1000.

Divide

Take the log of both sides.

Pull down the exponent.

Evaluate the left side

Evaluate the log on the right side

Divide both sides by 0.02531.

Divide and rearrange the equation.

So it will take about 27.61 years (a little over 27 and a half years) for $1,000 to become $5,000 at an interest rate of 6%

------------------------------------
b)

Start with the given equation.

Plug in , , and

Add

Divide both sides by 1000.

Divide

Take the log of both sides.

Pull down the exponent.

Evaluate the left side

Evaluate the log on the right side

Divide both sides by 0.04922.

Divide and rearrange the equation.

So it will take about 14.2 years (a little over 14 years) for $1,000 to become $5,000 at an interest rate of 12%
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