Why is more interest paid at the beginning of a loan versus the end of a loan?

Answer 1

More interest is charged at the beginning of a loan to appropriately cover the "average balance" of the principal. At the beginning of the loan, the entire principal is due, so one would pay more interest on that principal.

Using a simple credit card example, say one buys $1,200 of home furnishings at the beginning of the credit card cycle and decides to pay that balance off over time. The individual also commits to paying $150 per month until the balance is paid. Finally, the credit card charges 18% per year in interest and payments are made in the middle of the credit card cycle. So, putting it all together as follows:

Month BegBalance Purchases Interest Payment EndBalance AvgBalance

zero $0 $1,200 $0 $0 $1,200 $1,200

one $1,200 $0 $18 $150 $1,068 $1,134

two $1,068 $0 $17 $150 $935 $1,002

three $935 $0 $15 $150 $800 $868

four $800 $0 $13 $150 $663 $732

five $663 $0 $11 $150 $524 $594

six $524 $0 $9 $150 $383 $454

seven $383 $0 $7 $150 $240 $312

eight $240 $0 $5 $150 $95 $168

nine $95 $0 $2 $97 $0 $48

As one can see, the higher the average balance, the more one pays in interest. Home loans, auto loans and personal loans are all computed in a similar way (step-by-step), however, the total of the interest payments are added to the beginning principal then divided by the number of periods over which the loan is to be paid to get to a single payment. IN the above example, pretending that the loan was to be paid over nine (9) months, the monthly payment for an associated personal loan of $1,200 would have been $144 (as one can see, the final payment was less than the $150 usually paid). For perspective, the amount of interest paid in the first and last months would have been $18 and $2, respectively.

While we ignored the complexity of month-adjusted interest (months in which there are more days generate more days of interest), grace period (time allowed to pay a balance without incurring finance charges), and residual interest (the interest on the average balance for the month in which the bill was paid in full - would have been 72 cents in month ten), the idea is the same - bigger average balance - higher amount of interest paid.

The formula for computing periodic payments is presented as follows:

PMT = PRINCIPAL * ((1 / periodicrate) - (1 / ((1+periodicrate)^periods)))

[excel: '=pmt(periodicrate, periods, PRINCIPAL)']

where:

PMT is the monthly (periodic) payment

PRINCIPAL is the amount borrowed

periodicrate is the rate per period (e.g., 18% per year = 18%/12 = 1.5% per month)

periods is the number of periods in the loan (e.g., 9 months = 9 periods)

[finding interest payment: excel: '=ipmt(periodicrate, whichperiod, periods, PRINCIPAL)']

Where

whichperiod is the period for which you want to know the interest portion of the payment