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John Jamison wants to accumulate $62,154 for a down payment on a small business. He will invest $34,000 today in a bank account paying 9% interest compounded annually. Approximately how long will it take John to reach his goal? (Do not round intermediate calculations. Round your final answers to nearest whole dollar amount.)

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facundobuzzetti

Answer:

It will take him 7 years.

Explanation:

Hi! We need to calculate the amount of time that it requires an investment of $34000 to reach $62154 at an interest rate of 9% annually.

By using the formula of Present Value we can isolate n:

The formula is:

PV=Ct/[(1+r)^n]

Ct= cash flow at t time

r= rate

n= period of time

To calculate how many years, we need to isolate n from the PV formula:

n=[ln(Ct/PV)]/ln(1+r)

n=ln(62154 /34000 )/ln(1+0,09)

n=7

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