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: 0,000.00
Interest rate: 2.50%
Interest rate per period: 0.21% (2.50%/12)
Amortization: 25
Num of periods (months): 300 (25*12)
Monthly payment: ,121.54 (PMT(2.5%/12,25*12,-0,000))
Sum of all monthly pmts: 6,462.55 (300*,121.54)
FV function: 6,757.93 (FV(2.5%/12,25*12,0,-0,000))
However, FV(2.5%/12,25*12,21.54,-0,000) return [CO].
In other words, how come FV with "0" monthly payments evaluates at 6k, but FV with 21 monthly payment (which sums up to 6k and not 6k) evaluate at 0?
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You're comparing two different scenarios.
FV(2.5%/12,25*12,21.54,-0,000)
This says, I borrowed 0,000 and I want to know how much I will own if I pay off 21.54 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,-0,000)*300
This is the total amount you would pay if you paid 21.54 each month.
FV(2.5%/12,25*12,0,-0,000)
This says, I borrowed 0,000 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 (0,000) in a 2.5% portfolio, but withdraw 21 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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