Answer:
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
