# Math Help - Present value formula

1. ## Present value formula

Here's the problem that I'm looking at just to add some context to my question:

A borrower would like to borrow 30,000 at 8% for 5 years, but would like to pay only 2,000 for the first two years and then catch up with a higher payment for the final three years. What is the payment for the final three years?

I understand how to solve the problem using a financial calculator. I was just wondering if there is a formula for finding the the future value of the loan after the first two years.

I can write it out as:

$FV=(((30,000*(1.08))-2,000)*1.08)-2,000$

Which is fine if I only have to find the FV a couple years into the future.

I know that if there were no payments, it'd simply be:

$FV=30,000(1.08^{2})$

I'm just wondering if there is a similar formula that takes payments into account.

Thanks

Nevermind, I found a formula. For anyone interested it's

$BAL_{k}=PV(1+i)^{k}-(PMT*\frac{(1+i)^{k}-1}{i})$

2. ## Re: Present value formula

It is called a retrospective method of finding loan outstanding.

3. ## Re: Present value formula

Originally Posted by downthesun01
Nevermind, I found a formula. For anyone interested it's
$BAL_{k}=PV(1+i)^{k}-(PMT*\frac{(1+i)^{k}-1}{i})$
Notice that formula is a combination of 2 formulas: FV of AMOUNT less FV of PAYMENTS.
Works like this (looking at it as 2 accounts):
Code:
          LOAN                   SAVINGS
YR  INT(8%)   BALANCE    PAYMENT  INT(8%) BALANCE
0            30000.00                         .00
1  2400.00   32400.00    2000.00     .00  2000.00
2  2592.00   34992.00    2000.00  160.00  4160.00
So what is owing after 2 years: 34992 - 4160 = 30832