You need to accumulate $10,000. To do so, you plan to make deposits of $1,500 per year - with the first payment being made a year from today - into a bank account that pays 9.56% annual interest. Your last deposit will be less than $1,500 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal? Round your answer up to the nearest whole number.

5.4 years

Explanation:

Future value is the value of the calculated by compounding a specific present value using a specific discount rate

Payment = $1,500

Rate = 9.56%

Future value = $10,000

We will use the following formula to calculate the numbers of years.

Future Value = Payment x [ (1 + r) ^n - 1 / r ]

$10,000 = $1,500 x [ (1 + 9.56%) ^n - 1 / 9.56%

$10,000 x 9.56% / 1,500 = (1 + 9.56%) ^n - 1

0.6373 + 1 = 1.0956^n

1.6373 = 1.0956^n

Log 1.6373 = n log 1.0956

n = log 1.0956 / Log 1.6373

n = 5.4 years