Question

QUESTION 18

a. Based on a​ 30-day month and a​ 365-day year, if you put ​$1712 per month​ (first payment a month from​ today) into an investment account that earns 9.8​% ​APR, compounded daily​, how much will you have 11 years from​ today? ​ (Rounded to the nearest​ dollar)

b. If you invest ​$2928 for 4 years at 11​% per​ year, and then the money stays invested and earns 6.1​% per year for 5 more​ years, what would be your annual​ (average) rate of return for the entire 9 ​years? ​ (In percent, rounded to 3​ decimals.)

Answer 1

(a) APR = 9.8 %, Compounding Frequency: Daily, Applicable Periodic Interest Rate = (1.098)^(1/365) - 1 = 0.00026 or 0.026 %

Monthly Deposits = $ 1712, Deposit Tenure = 11 x 12 = 132 months

Therefore, Total Future Value of Deposits = 1712 x (1.00026)^(131) + 1712 x (1.00026)^(1711) +.........+ 1712 = 1712 x [{(1.00026)^(132) - 1} / {1.00026 - 1}] = $ 229818.26897 ~ $ 229818

(b) Periodic Investment = $ 2928, Initial Tenure = 4 years and Initial Interest Rate = 11%, Final Tenure = 5 years and Final Rate = 6.1 %

Total Future Value of Annual INvestments at the end of Year 4 = 2928 x (1.11)^(3) +...........+ 2928 = 2928 x [{(1.11)^(4)-1}/{1.11-1}] = $ 13790.09

Future Value at the end of Year 9 = 1370.09 x (1.061)^(5) = $ 18541.467