Question

Problem 2-13 (LO2.4) Brenda plans to reduce her spending by $90 a month. What would be the future value of this reduced spending over the next 10 years? (Assume an annual deposit to her savings account, and interest rate of 4 percent.) Use Exhibit 1.B. (Round time value factor to 3 decimal places and final an annual answer to 2 decimal places.) Future value

Answer 1

The solution to this question involves certain assumptions. The first assumption would be that current time is t=0 or beginning of the first year and the first deposit (savings through expense reduction) comes in at t=1year or end of this first year. Further, it is assumed that all monthly deposits are accumulated and deposited in one go into the savings account annually.

Monthly Savings = $ 90, Accumulated Annual Savings = 90 x 12 = $ 1080 and Annual Interest Rate = 4 %

Tenure of Deposits = 10 years

Total Future Value of Deposits = 1080 x (1.04)^(9) + 1080 x (1.04)^(8) + .....+ 1080 x (1.04)^(2) + 1080 x (1.04) + 1080 = =[{(1.04)^(10) - 1} / {1.04-1}] x 1080 = $ 12966.60