Question

college question: when jack started his job working for an industrial manufacturing company, he contributed $211 at the end of each month into a savings account earned 2.4% interest compounded monthly for 7 years. at the end of the 7th year, jack was laid off. to help meet family expenses, jack withdrew $295 from the savings account at the end of each month for 2 years. At the end of the second year of being unemployed, jack found another job and started contributing $138 back into the savings account at the end of each month for the next six years. How much money would he have in the account

Answer 1

I would solve this problem in three parts
1)First job
2)laid off
3) second job

Answer 2

I will also assume that he started the account with 0 balance

Answer 3

ok ill give it a try on the tvm solver

Answer 4

Post your results

Answer 5

im stuck. im trying to find out how to the laid off part. i first tried to just do 24 x 295 and that would be the amount that he took out total, but at the same time the account is earning interest so im not sure what to do

Answer 6

wow this is really complicated lol

Answer 7

Deposit= D
R = Rate

First Month - D
Second Month - D+D(1+R) = D(1+(1+R))
Third Month - D(1+(1+R)+(1+R)^2)
We see a pattern
Nth Month - D(1+(1+R)+(1+R)^2+(1+R)^3+.....+(1+R)^N-1)
You can add them up to 7 years but there is a short cut.
(1+y+....+y^(n-1))(1-y)= (1-y^n)

Using it on our equation..
D(1+(1+R)+(1+R)^2+(1+R)^3+.....+(1+R)^N)=
D [ (1-(1+R)^N)/(1-(1-R))]
D(-(1-(R+1)^N)/R)

Answer 8

when i used the tvm solver i got n= 84 (12)(7) I%= 2.4 pv= 0 pmt= -211 and he would end up having 19278.88 before he got laid off?

Answer 9

"he contributed $211 at the end of each month into a savings account earned 2.4% interest compounded monthly for 7 years."

Let plug in number
D(-(1-(R+1)^N)/R)
211(-(1-(.024/12+1)^63)/(.024/12))=$19278
That's how much he had before he got laid off

Answer 10

so you were wrong lol thats not the part i needed help with i needed help with the part where here withdrew 295

Answer 11

Here is formula, to avoid confusion I won't include the derivation(let me know if you're interested)
P= Balance
R= Interest( For Month)
N= Number of Month
W- Withdrawal

\[P(1+R)^N-w\left(\frac{\left(1-(1+R)^N\right)}{-R}\right)\]

Answer 12

Plugging in
\[19278\left(1+\left(\frac{.024}{12}\right)\right)^{24}-295\left(\frac{\left(1-\left(1+\left(\frac{.024}{12}\right)\right)^{24}\right)}{-\left(\frac{.024}{12}\right)}\right)\]
I got 12979.7

Answer 13

Excel agrees with me

Answer 14

Any question?

Answer 15

yes
if he withdrew 295 for 2 years, how is there more money in the account than before?

Answer 16

Before there was $19278 after two years of withdrawal there is $12979.7; certainly no more than before.

Answer 17

Any other?

Answer 18

ohoh okay thanks i read it wrong
ill go ahead and try to finish the last step now

Answer 19

Thanks for posting, a real interesting problem (and solution)