(5) A series of monthly cash flows is deposited into an account that earns 12% a

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 $5,200 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

Step 1: Calculate Future Value of Monthly Deposits

The future value of an annuity can be calculated with the use of following formula:

Future Value of an Annuity = Amount*[((1+Rate)^(Period)-1)/Rate]

Here, Amount = $2,500, Rate = 12%/12 = 1% and Period = 6 (Total Number of deposits in 2013) + 6*12 (Total Number of Deposits from 2014 to 2019) + 3 (Total Number of Deposits in 2020) = 81 months

Using these values in the above formula, we get,

Future Value of Monthly Deposits = 2,500*[((1+1%)^81-1)/1%] = $309,720.59

_____

Step 2: Calculate Effective Quarterly Interest Rate

The effective quarterly interest rate is calculated as below:

Effective Quarterly Interest Rate = (1+Monthly Interest Rate)^3 - 1 = (1+1%)^3 - 1 = 3.03%

_____

Step 3: Calculate Future Value of Quarterly Withdrawals

The future value of quarterly withdrawals can be calculated with the use of same formula as provided in step 1.

Here, Amount = $5,200, Rate = 3.03% and Period = 26 (Total number of quarters between December 1, 2013 and March 1, 2020)

Substituting values in the formula for future value of annuity, we get,

Future Value of Quarterly Withdrawals = 5,200*[((1+3.03%)^26 - 1)/3.03%] = $201,303.90

_____

Step 4: Calculate Balance Amount in Account After Last Withdrawal

The balance amount in account after last withdrawal is calculated as below:

Balance Amount in Account = Future Value of Monthly Deposits - Future Value of Quarterly Withdrawals = 309,720.59 - 201,303.90 = $108,416.69 or $108,417

_____

Notes:

1) There can be a slight different in final answer on account of rounding off values.

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