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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Business

Chloe Obrien

30 July, 19:19

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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Answers (1)

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Mauricio Mercer · Answer 1

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