$4000 is deposited in an account that pays an APR of 7.7​% compounded annually. How long will it take for the balance to reach ​$100, 000​?

Question

It will take years for the balance to reach

​$100,000.

​(Round up to the nearest​ year.)

Answer 1

To get this answer to this we have to know the formula to figure out future value.

Future Value = Present Value of Money *(1 + APR)ⁿ written as FV = PV(1+r)ⁿ

Once we know this equation we can just plug and chug the equation and solve for n.

FV = $100,000

PV = $4,000

r = 0.077 (7.7% represented as a decimal)

Giving us the equation 100,000 = 4,000(1+.077)ⁿ

100,000/4,000 = (1.077)ⁿ

25 = 1.077ⁿ

To solve for n now we take the natural log of 25 and divide that by the natural log of 1.077

ln(25)/ ln(1.077) = n

This should give you a value of 43.4 years or 44 years.

It will take 44 years for $4,000 to become $100,000 with an APR of 7.7%