Charter has been contributing $900 at the end of each month for the past 15 months to a savings plan that earns 4% compounded monthly. What amount will he have one year from now, if he continues with the plan?
A) $25 382.84
B) $13 819.60
C) $6898.05
D) $12 669.42
E) $13 500

Question

Quizplus · Accepted Answer

Using the formula for compound interest:

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

where:

A = the amount after time t
P = the principal amount (the initial amount invested)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the time (in years)

In this case, P = $900, r = 0.04 (4% as a decimal), n = 12 (compounded monthly), and t = 1 (one year). We can plug these values into the formula:

A = $900(1 + 0.04/12)^(12*1)
A = $900(1.003333)^12
A = $900(1.043183)
A = $9388.48

Therefore, Charter will have $9388.48 after one year if he continues with the savings plan. However, the question asks for the amount one year from now, which is actually 15 months from the start of the plan. We can use the formula again with t = 15/12 = 1.25:

A = $900(1 + 0.04/12)^(12*1.25)
A = $900(1.004167)^15
A = $900(1.051523)
A = $9477.37

Therefore, Charter will have $9477.37 one year from now (15 months from the start of the plan) if he continues with the savings plan. However, none of the answer choices match this value exactly. The closest choice is A) $25 382.84, but this is clearly an error in calculation. The correct answer is A) $9477.37.

Charter Has Been Contributing $900 at the End of Each