(5) A series of monthly cash flows is deposited into an account that earns 12% a
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Question
(5) A series of monthly cash flows is deposited into an account that earns 12% annual nominal interest compounded monthly. Each monthly deposit is equal to $2,500. The first monthly deposit occurred on July 1, 2013 and the last monthly deposit will be on March 1, 2020. The account (the series of monthly deposits, 12% nominal interest, and monthly compounding) also has equivalent quarterly withdrawals from it. The first quarterly withdrawal is equal to S5,200 and occurred on December 1, 2013. The last $5,200 withdrawal will occur on March 1, 2020. How much remains in the account after the last withdrawal?Explanation / Answer
Jun 01, 2013; t = 0
Jul 01, 2013; t = 1
Aug 01, 2013; t = 2
Dec 01, 2013; t = 6
Mar 01, 2020; t = 6 + 12*6 + 3 = 6 + 75 =81
Compute FV of deposits:
Monthly interest rate = 1%
FV = (2500/0.01)*(1.01^81 - 1) = 309720.59
Compute FV of withdrawals:
Quarterly interest rate = 3%
Number of quarters = (75 + 1)/3 = 25 + 1/3
FV = (5200/0.03)*(1 - 1/1.03^25) + 5200*1.03^(25 + 1/3) = 101543.82
Money remains on March 01, 2020 = 309720.59 - 101543.82 = 208,176.77
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