Question

If Mike deposits 200 dollars at the end of each month in a savings account earning interest at a nominal rate of 4.1 percent per year compounded monthly, how much will he have on deposit in his savings account after 8 years, assuming that he makes no withdrawals during that period?

Answer 1

The formula for calculating a monthly annuity is shown in the attached graphic.
First, let's just calculate it for yearly compounding.

.0410yearly = .0034166667 monthly

Total = [200*(1.0034166667)^97)-1)/.0417793008] -200

Wow, I just spent about 30 minutes typing about 10 lines of calculation that ended up wrong.

I think the answer should be about 20,031.11
I'm quitting for now.

Answer 2

Lol Right? The fact that 200 dollar that is added at every month is messing up the formula but I can probably write a computer program to calculate the final

Answer 3

lol sorry but 20031.11 is not the answer

Answer 4

Lin, does the question state the the interest rate is added after the 200 dollars is added at the end of every month or BEFORE it is added?

Answer 5

i dont recall my prof teaching how to calculate this kind of question, so i tried using the continuous compounding formula but obviously that didnt make sense :(

Answer 6

theres no further specification, but i would assume that it is added after the $200 just because during the first month, there wouldnt be anything there?!!

Answer 7

Okay so after much much MUCH research, I think have an attempt at this. Instead of using just one formula to find out the solution, we had to use TWO OF EM! CRAZYYY! anyways:
FutureValuea=((1+i)^n) × a
FutureValueb=P×((1+i)2−1)i
a=initialDeposit
P=monthlyDeposit
i=0.003416666667
n = 8 x 12
Total =
FutureValuea+FutureValueb
Please try that and see if it works.

Answer 8

heres what i tried!
Future Value A = ((1+0.00341666668)^96)x200
Future Value B = 200 x ((1+0.00341666667) x 2-1) x 0.003416666667
then A + B = 278.1706 but thats not correctly answer either! :O

Answer 9

oh I'm sorry for Future Value B that the equation should be:

\[P \times \frac{( (1+i)^{n} -1) }{ i }\]
for some reason when I copied and pasted from my earlier fail attempt. It didn't copy correctly.

Answer 10

200 x [(1+(0.041/12)^96 -1]/(0.041/12) right??

Answer 11

equals to 22677.8404

Answer 12

OMG!!! THANK YOU SO MUCH!!!!

Answer 13

but just for confirmation, is that the annuity formula?

Answer 14

You're very welcome =)

And I'm not sure on the names of the formulas, but "FutureValueA" represented the future value you would get if you did the monthly compound without the monthly contribution.

and the "FutureValueB" was for the monthly contribution that you would add with the interest.

I believe that is what I saw when I was researching on this question. Best of luck to ya.

Cheers!

Answer 15

once again!!! thank you so much!!!! ;))))))