Question

re. When Jack started his job working for an industrial manufacturing company, he contributed $550 at the end of each three months into a savings account that earned 2.4 % interest compounded quarterly for 12 years. At the end of the 12th year, Jack was laid off. To help meet family expenses, Jack withdrew $700 from the savings account at the end of each three months for 3 years. At the end of the third year of being unemployed, Jack found another job and started contributing $315 back into the savings account at the end of each three months for the next seven years. Do the following: A. How much money would he have in the account at the end of the seven 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 22 years of the account. (12 points)

Answer 1

The major formula used are

FVOrdinary Annuity​=C×[i(1+i)n−1​]

where:

C=Cash flow per period;

i=Interest rate;

n=Number of payments​ ;

the case can be divided into 3 parts

1st... the present value of the fund (deposits) at the end of 12 years.

2nd... the amount is withdrawn after he lost his job and had to withdraw from his annuity.

3rd... the amount he added when he got a new job.

Part 1:

FV of annuity where

C= $550

i= 2.4% annually or 2.4%/4=>.6% .;

n= 12*4=>48 periods

placing the values in the formula you will get around $30,489.25 (i.e 550 * (((1+.006)^48)-1)/.006) )

Part 2:

withdrawals will remove value from your fund and should be considered as a negative annuity while the fund still compounds at a normal rate

hence the value of the fund after 3 years will be( without the negative annuity): $30,489.25 (1.006)^(3*4) = $32,758.39

Diminishing annuity: using the same formula we get $8,734.92 (i.e 700 * (((1+.006)^12)-1)/.006) )

the value of the fund after 3 years will be $24,023.47

Part 3:

forward anuity of $315 for 7 years= $9,630.44 (i.e 315 * (((1+.006)^28)-1)/.006) )

Value of gund compunding for 7 years= $24,023.47*(1.006)^(7*4) = $28,403.98

value of fund $29,367.42

Solution 1: $29,367.42

Solution 2: $29,367.42 - (550*48 -700*12 +315*28)= $2,547,42