Loan Payment with Equal Principal

Calculates the payments on an equal-principal loan. The principal repaid each month is fixed at the loan amount ÷ the number of payments, with interest on the outstanding balance added on top. As the balance falls, each payment gets a little lighter.

An equal-principal loan repays the same amount of principal every month. Where a fixed-instalment loan holds the payment itself steady, this method holds the principal steady instead. Interest is charged on whatever is still owed, so as the balance falls the interest falls with it, and each payment is a little lighter than the last.

M_k = \dfrac{P}{n} + B_k \times i

$M_k$ is the payment in month $k$
$P$ is the loan amount
$n$ is the number of payments, the number of years times 12
$B_k$ is the balance just before payment $k$
$i$ is the monthly rate, the annual rate (%) divided by 100 and again by 12

The balance $B_k$ falls by $P \div n$ each month, so it starts at $P$ and ends at $P \div n$ .

Total interest

The interest differs every month, but there is no need to add up 420 separate figures. The balance falls by the same step each time, which makes it an arithmetic sequence, and such a sequence is summed by adding the first and last terms, multiplying by the count and halving.

I = i \times P \times \dfrac{n + 1}{2}

$I$ is the total interest.

Example

With a loan of 30000000, an annual rate of 1.5% and a term of 35 years, there are 420 payments and the monthly rate is 0.00125.

The principal repaid each month is $30000000 \div 420$ , about 71429. The first payment adds interest on the full 30000000, which is 37500, giving about 108929. By the final payment only 71429 is still owed, so the interest is just 89 and the payment falls to about 71518. The total repaid is about 37893750, of which about 7893750 is interest.

Compared with fixed instalments

The same loan repaid in fixed instalments costs 91855 every month and about 8579239 in interest. The equal-principal method costs 7893750, saving about 685489.

The gap comes from how fast the principal shrinks. With fixed instalments, most of an early payment goes on interest and the principal barely moves. Equal principal chips away the same amount from the very first month, so the balance carrying interest gets small sooner.

Points to watch

The trade-off is a heavier first payment: 108929 against 91855 here, a difference of about 17000. Lenders often assess affordability on that first figure, so choosing equal principal can lower the amount you are allowed to borrow.

This is the method whose burden is heaviest at the start, so check that the payment is comfortable on the income you have when repayment begins. The calculation assumes the rate never changes, and it excludes guarantee fees, arrangement fees, insurance and tax.