You deposit $1,000 today and want to save $100 each month beginning one month from today. Your account earns a 5% annual interest rate. How long will it take you to accumulate $5,000?
A) 29.3 months
B) 35.7 months
C) 42.6 months
D) 52.1 months

Question

Quizplus · Accepted Answer

Using the formula for Future Value of an Annuity,

FV = Pmt x [(1 + r)^n - 1] / r + PV x (1 + r)^n

where FV = 5000, Pmt = 100, r = 0.05/12 (monthly interest rate), PV = 1000, and n = number of months, we can solve for n.

5000 = 100 x [(1 + 0.05/12)^n - 1] / (0.05/12) + 1000 x (1 + 0.05/12)^n

After some algebraic manipulation and rounding up to the nearest whole number, we get:

n = 36 months or 3 years

Therefore, it will take 36 months or 3 years to accumulate $5,000. The closest answer choice is (B) 35.7 months.

You Deposit $1,000 Today and Want to Save $100 Each