Question

Carmen is planning to invest $200 in a retirement account at the end of each month for the next 20 years. The account is earning 3.15% interest, compounded annually. He used the following formula and variables to solve for the future value of the account after 20 years.



FVOA = Future Value of an Ordinary Annuity
C = 200
n = 1
t = 20
i = 0.0315

He found that the future value of this account will be $5456.83. Is Carmen’s solution correct? If not, explain what he did wrong and provide the correct solution.

Answer 1

Well n should aactually be 240 since it is 20yrs at 12 month's per year

Answer 2

Payment should be -200 since it is a cash outflow

Answer 3

the future value??

Answer 4

You can use the geometric summation of:

\[\sum_{n = 1}^{240} $200(1 + \frac{0.0315}{12})^n\]\[$200(1 + \frac{0.0315}{12})[\frac{1 - (1 + \frac{0.0315}{12})^{240}}{1 - (1 + \frac{0.0315}{12})}]\]
Which comes out to approximately $66,922.75

Answer 5

alright thanks

Answer 6

Just use financial concept it's way easier

Answer 7

ok i'll remember that

Answer 8

I derived the summation from the compound interest formula
\[A = P(1 + \frac{r}{n})^{nt}\]
There is no other way to do the problem except with Calculus, geometric summation is the most simplest method

Answer 9

oh ok got it

Answer 10

Use ur financial calculator it's way faster

Answer 11

i am now

Answer 12

Did you get it

Answer 13

dont know yet i'll find ouy in a couple of minutes