Question

You decide to deposit $400 at the end of each year into an account that pays 8.9% interest. If the first deposit occurs one year from today, how many years will it take to accumulate a balance of $6,000 ? Answer Format: Enter your answer as a number rounded to 2 decimal places. An answer of 23.456 would be entered as 23.46 .

Answer 1

To accumulate a balance of $6,000 with a $400 deposit at an 8.9% interest rate, it will take approximately 12.59 years.

Step-by-step explanation:

To find out how many years it will take to accumulate a balance of $6,000, we can use the formula for compound interest:

A = P(1+r)^n

Where A is the desired balance, P is the deposit amount, r is the interest rate, and n is the number of years.

In this case, we have:

$6,000 = $400(1+0.089)^n

Dividing both sides by $400 gives us:

15 = (1+0.089)^n

Taking the logarithm of both sides gives us:

n log(1+0.089) = log(15)

Dividing both sides by log(1+0.089) gives us:

n = log(15) / log(1+0.089)

Using a calculator, we find that n is approximately 12.59 years. Therefore, it will take approximately 12.59 years to accumulate a balance of $6,000.