Financial Calculations: What am I not understanding?

Question

Given a loan of $1,000  with the following terms

- AMT = $1,000.00

- NPER  = 60 (5 yrs on mthly pymts)

- RATE = 8% (Annual rate) (i.e. .08/12 per term)

Then:

- PMT = $20.28

- Total AMT repaid = (60 * $20.28)  = $1,216.58

All well and good so far....

Am assuming that the future value (FV) of the $1,000.00 using the same values as for the loan, would likewise come out to $1,216.58.

But instead:

- RATE = .08/12

- NPER = 60

- PMT = $20.28

- PV = $1,000.00

Then FV comes out as:   -$2,979.69

This doesn't make sense.

If my spreadsheet isn't broke, then my understanding of PMT and FV calculations is broke!

Frank Jiang · Answer

Here's your fundamental problem.  Your total amount repaid does NOT equal the future value.  The FV is the 1489.84 that you calculated.  You can get the same answer just growing 1000 @ 8% for 5 years [1000 * (1 + (8%/12)^60)].

The reason it's not equal to the 1,216.58 total payments is because a portion of this 1,216.58 is paid at an earlier point than your FV point (5 years in the future) and thus those payments are subject to Time Value of Money.  Basically, the first payment you make of 20.28 has to be grown @ 8 percent for the next 4 yr 11mo to tie back to your FV.

Make sense?

Pete Smith · Answer

Jim

Thanks for the feedback. I did change the payment to 0 so the values then were:

- RATE = .08/12

- NPER = 60

- PMT = 0

- PV = -$1,000.00

Then FV comes out as:   $1,489.85

Closer to the original, but still not equal. I'm still not understanding why It's not producing the same result.

Jimmy Murray · Answer

The only thing that I can think of is that your FV wouldn't include a payment. The payment should be $0 to get to your previous answer