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 June 1, 2008 and the last monthly deposit will be on January 1, 2015. The account also has equivalent quarterly withdrawals from it. The first quarterly withdrawal is equal to $5,000 and occurred on October 1, 2008. The last $5,000 withdrawal will occur on January 1, 2015. How much remains in the account after the last withdrawal?

The amount left in the account after last withdrawal is $61,945

Explanation:

The first monthly deposit occurred on June 1, 2008 and the last monthly deposit will be on January 1, 2015 = 80 deposit

Monthly deposit = 2,100

Interest rate = 12% / 1% per month

Firstly, we calculate the future worth of the monthly deposit

FW = A(F/A, i, n)

A = 2,100, i = 1%, n= 80

FW = $2100*[(1+0.01)^80 - 1 / 0.01]

FW = $2100*[2.216715 - 1 / 0.01]

FW = $2100*(121.671)

FW = $255,509.10

We calculate the effective interest rate

i(effective) = (1 + i nominal monthly interest rate)^n - 1

i `%, n = 3(no of months in quarter)

i (effective) = (1+0.01)^3 - 1

i (effective) = (1.01)^3 - 1

i (effective) = 1.030301 - 1

i (effective) = 0.030301

i (effective) = 3.0301%

The effective quarterly interest rate is 3.0301%

We calculate the future worth of the quarterly drawings

FW = A[(1+i)^n - 1 / i]

A = 5,000(drawing), i = 3.0301%, n = 26(number of drawings)

FW = 5,000*[(1+0.030301)^26 - 1 / 0.030301]

FW = 5,000*[2.17303717 - 1 / 0.030301]

FW = 5,000*(38.71282)

FW = $193,564.10

The future worth of the quarterly withdrawal is $193,564.10

We calculate the amount left in the account after last withdrawal

Amount left in account = FW(monthly deposits) - FW(quarterly drawings)

Amount left in account = $255,509.10 - $193,564.10

Amount left in account = $61,945

Thus, the amount left in the account after last withdrawal is $61,945

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