Question

1. When Jack started his job working for an industrial manufacturing company, he con $240 at the end of each month into a savings account that earned 2.3 % interest compounded monthly for 6 years. At the end of the 6th year, Jack was laid off. To help meet family expenses, Jack withdrew $250 from the savings account at the end of each month for 1 years. At the end of the first year of being unemployed, Jack found another job and started contributing $180 back into the savings account at the end of each month for the next five years. Do the following A. How much money would he have in the account at the end of the five years after returning to work)? Use the TVM Solver to solve this problem. Show all the necessary work that you need perform to arrive at the answer. (12 points) B. Determine the total interest that Jack earned during the 12 years of the account. (12 points)

Answer 1

1]

A]

Money in account at end of 6 years is calculated as below :

N = 72 (6 years with 12 monthly deposits each year. Total number of deposits = 6 * 12 = 72)

I/Y = 0.1917 (monthly interest rate = annual rate / 12 = 2.3%/12 = 0.1917%)

PMT = -240 (Monthly deposit. This is entered with a negative sign because it is a cash outflow for Jack)

CPT --> FV

FV is calculated to be $18,510.13.

B]

Money in account at end of 7 years is calculated as below :

N = 12 (1 year with 12 monthly withdrawals each year)

I/Y = 0.1917 (monthly interest rate = annual rate / 12 = 2.3%/12 = 0.1917%)

PMT = -250 (Monthly withdrawal. This is entered with a negative sign because it is a cash outflow from the account)

PV = 18510.13 (Money in account at end of 6 years. This is entered with a positive sign because it is like a deposit into the account at the end of the 6th year)

CPT --> FV

FV is calculated to be $15,908.55.

Money in account at end of 12 years is calculated as below :

N = 60 (5 years with 12 monthly deposits each year. Total number of deposits = 5 * 12 = 60)

I/Y = 0.1917 (monthly interest rate = annual rate / 12 = 2.3%/12 = 0.1917%)

PMT = -180 (Monthly deposit. This is entered with a negative sign because it is a cash outflow for Jack)

PV = -15908.55 (Money in account at end of 6 years. This is entered with a negative sign because it is like a deposit into the account at the end of the 7th year)

CPT --> FV

FV is calculated to be $29,279.32.

Interest earned during first 6 years =  Money in account at end of 6 years - total deposits during first 5 years

Interest earned during first 6 years = $18,510.13 - ($240 * 72)

Interest earned during first 6 years = $1,230.13.

Interest earned during 7th year = Money in account at end of 7 years - (Money in account at end of 6 years - total withdrawals during 7th year)

Interest earned during 7th year = $15,908.55 - ($18,510.13 - ($250 * 12))  

Interest earned during 7th year = $398.42

Interest earned during Years 8 to 12 = Money in account at end of 12 years - Money in account at end of 7 years - total deposits during Years 8 to 12

Interest earned during Years 8 to 12 = $29,279.32 - $15,908.55 - ($180 * 60)

Interest earned during Years 8 to 12 = $2,570.77

Total interest earned during 12 years =  $1,230.13 + $398.42 + $2,570.77

Total interest earned during 12 years =  $4,199.32