# Why SUM(PMT) is not identical to FV?

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?

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%.

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%.
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.