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Thumbs up Answer: What is the real math behind PMT and IPMT function?

Explanation of PMT and IPMT Functions in Excel

PMT stands for Payment, and it calculates the periodic payment for a loan or investment based on a constant interest rate, constant payments, and a constant loan amount. The formula for PMT is:

Formula:
PMT = (rate present value) / (- (rate)^(-n)) 
Whe
- rate is the interest rate per period
- present value is the loan amount or present value of the investment
- n is the total number of payment periods

For example, if you have a $10,000 loan with a 5% annual interest rate and a 5-year term, the PMT formula would be:

Formula:
PMT = (0.05/12 10000) / (- (0.05/12)^(-5*12))
PMT = $188.71 
This means that you would need to make monthly payments of $188.71 to pay off the loan in 5 years.

IPMT stands for Interest Payment, and it calculates the interest portion of a loan or investment payment for a specific period. The formula for IPMT is:

Formula:
IPMT rate period present value 
Whe
- rate is the interest rate per period
- period is the payment period for which you want to calculate the interest
- present value is the loan amount or present value of the investment
- n is the total number of payment periods

For example, if you want to calculate the interest portion of the third payment for the same $10,000 loan with a 5% annual interest rate and a 5-year term, the IPMT formula would be:

Formula:
IPMT 0.05/12 10000 / (5*12)
IPMT = $41.67 
This means that the third payment of $188.71 would consist of $41.67 in interest and $147.04 in principal.
  1. Use the PMT function to calculate the periodic payment for a loan or investment based on a constant interest rate, constant payments, and a constant loan amount.
  2. Use the IPMT function to calculate the interest portion of a loan or investment payment for a specific period.
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