A series of monthly cash flows is deposited into an account that earns 12% nomin

Question

A series of monthly cash flows is deposited into an account that earns 12% nominal interest compounded monthly. Each monthly deposit is equal to $2,100. The first monthly deposit occurred on July 1, 2013 and the last monthly deposit will be on February 1, 2020. The account (the series of monthly deposits, 12% nominal interest, and monthly compounding) also has equivalent quarterly withdrawal from it. The first quarterly withdrawal is equal to $5,000 and occurred on November 1, 2013. The last $5,000 withdrawal will occur on February 1, 2020. How much remains in the account after the last withdrawal?

Explanation / Answer

This problem has two Future Value annuities.

First of deposites, second of withdrawals.

FV = A [ (1+r)^n -1] / r

monthly rate, r = 12% / 12 = 1% = 0.01

quarterly rate, i = (1+0.01)^3 = 3.0301

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Deposits:

n = 6 full years, 6 months in 2013, and 2 months in 2020 = 80 months

FV = 2,100 [ (1+0.01)^80 -1] / 0.01

FV = 255,510.20

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Withdrawals:

n = 6 full years, and one quarter from november to february = 25

FV = 5,000 [ (1+0.030301)^25 -1] / 0.030301

FV = 183,018.46

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Money left in Account = Deposits - Withdrawls

Money left in Account = 255,510.20 - 183,018.46

Money left in Account = 72,491.74

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