Question

​$4000 is deposited in an account that pays an APR of 8.4​% compounded annually. How long will it take for the balance to reach ​$120,000​?

Answer 1

Answer: number of years that it will take for the balance to reach ​$120,000 is 42 years

Step-by-step explanation:

Initial amount deposited into the account is $4000. This means that the principal is $4000

P = 4000

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 8.4%. So

r = 8.4/100 = 0.084

Let the number of years that it will take for the balance to reach ​$120,000. It means that it was compounded for a total of t years.

Amount, A at the end of t years is $120,000

The formula for compound interest is

A = P(1+r/n)^nt

120000 = 4000(1 + 0.084/1)^1×t

120000/4000 = 1.084^t

30 = 1.084^t

t = 42 years