SOLUTION: How much must be deposited at the end of each month for 3.5 years to accumulate to $1,801.00 at 8% compounded monthly?

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Question 1194508: How much must be deposited at the end of each month for 3.5 years to accumulate to $1,801.00 at 8%
compounded monthly?

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

1 year = 12 months
3.5*1 year = 3.5*12 months
3.5 years = 42 months

We want the future value to be $1,801 and have it occur at the 42 month mark.
The annual interest rate in decimal form is r = 0.08

Divide by 12 to get the monthly version: r/12 = 0.08/12 = 0.00666666666667
which is approximate.

The future value annuity formula to use is this
FV = P*( (1+i)^n - 1)/i
This is an ordinary annuity and not "annuity due".
This is because the deposits happen at the end of each month, rather at the beginning.

In this case,
FV = future value = 1801
P = unknown monthly deposit
i = 0.00666666666667 approximately
n = 42 months

Let's solve for P
FV = P*( (1+i)^n - 1)/i
1801 = P*( (1+0.00666666666667)^42 - 1)/0.00666666666667
1801 = P*48.2851385181578
P = 1801/48.2851385181578
P = 37.2992613311594
P = 37.30

Answer: $37.30