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.)

Question

Business

Daisy Austin

28 March, 17:14

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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Aria Hutchinson · 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