1

I'm exploring financial functions in a spreadsheet. When I use FV, which is based on FV = PV*(1+r)^n I get a different number than when using PMT and multiplying by the number of periods.

For example:

  • Principal: $250,000.00
  • Interest rate: 2.50%
  • Interest rate per period: 0.21% (2.50%/12)
  • Amortization: 25
  • Num of periods (months): 300 (25*12)
  • Monthly payment: $1,121.54 (PMT(2.5%/12,25*12,-$250,000))
  • Sum of all monthly pmts: $336,462.55 (300*$1,121.54)
  • FV function: $466,757.93 (FV(2.5%/12,25*12,0,-$250,000))
  • However, FV(2.5%/12,25*12,$1121.54,-$250,000) return $0.

In other words, how come FV with "0" monthly payments evaluates at $466k, but FV with $1121 monthly payment (which sums up to $336k and not $466k) evaluate at 0?

2

You're comparing two different scenarios.

FV(2.5%/12,25*12,$1121.54,-$250,000)

This says, I borrowed $250,000 and I want to know how much I will own if I pay off $1121.54 each month for 25 years and the interest rate is 2.5%.

That means you're gradually reducing your principal, so the interest accruing each month gradually reduces.

PMT(2.5%/12,25*12,-$250,000)*300

This is the total amount you would pay if you paid $1121.54 each month.

FV(2.5%/12,25*12,0,-$250,000)

This says, I borrowed $250,000 and I want to know how much I will own if I don't pay anything for 25 years and the interest rate is 2.5%.

That means the amount you owe continues to grow, so the extra interest each month will be larger.

This is conceptually similar to a scenario in which you invest a sum of money ($250,000) in a 2.5% portfolio, but withdraw $1121 on a monthly basis: you would end up with much more if you didn't withdraw at all and waited instead.


The difference between the two scenarios is why, if you take out a mortgage, you should always pay your monthly amount! And why, if you don't, the bank will come after you and foreclose!

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