Question

You've graduated from college and landed a good job. You want to replace your​ car, but​ don't want to take out a car loan. ​ Instead, you decide to invest ​$100​ per month in the stock market and hope to ​earn 6​%. If the market performs as​ you're hoping, how many years will it take to accumulate ​$15 comma 000​? Ignore taxes.

Answer 1

3 years 3.5 months or 3.29 years

Step-by-step explanation:

A fix Payment for a specified period of time is called annuity. The Compounding of these payment on a specified rate is known as Future value of annuity. In this question $100 per month payment at 6% interest rate is also an annuity.

We can calculate numbers of years needed to make desired amount by future value annuity formula.

Formula for Future value of annuity is as follow

Future value of annuity = FV = P x ( [ 1 + r ]^n - 1 ) / r

Where

P = Annual payment = $100

r = rate of return = 6%

Placing Value in the formula

$15,000 = $100 x ( [ 1 + 6% ]^n - 1 ) / 6%

($15,000 x 6%) / $100 = ( [ 1 + 0.06 ]^n - 1 )

9 = [ 1.06 ]^n - 1

9 + 1 = [ 1.06 ]^n

10 = [ 1.06 ]^n

log 10 / = n log 1.06

n = log 10 / log 1.06

n = 39.52 months

n = 3 years 3.5 months or 3.29 years