How do I calculate the future value of this account?

Question

Suppose I'm earning 2.5%/week on my account whose principal value is $500. Every two weeks I add $150 to the account. What will the value of the account be after 1 year? What is the formula (Pe^Rt ?) and how do I apply it?

Answer 1

You are going to need another formula because 

there are bi-monthly contributions which

increases the principal, hence the interest.

 

P(1 + r)^Y + c[ ((1 + r)^Y - 1) / r ]

 

where P is the starting principal, in this case P=$500

r is the interest rate, in this case r=2.5% = 0.025

c is the contribution amount , in this case $150.

 

HOWEVER, because the interest accumulates weekly

and the contribution is made EVERY OTHER WEEK,

the Y values in the formula are different.

(They use Y because typically, the interest accumulates

 annually or once per year, for a specified number of years, Y) 

 

We need to modify the formula slightly for this purpose.

P(1 + r)^t + c[ ((1 + r)^T - 1) / r ]

 

lower case t , t = 52 because the weekly interest

on the principle accumulates for one year or 52 weeks

 

capital T, T = 26, because the contribution is

made every other week for 1 year, or 26 weeks

 

$7207.32

 

Here's where I found the formula:

http://www.moneychimp.com/articles/finworks/fmbasinv.htm