# 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%.

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!