Calculate, organize and pay off your loans with ease

How a fixed loan payment is calculated

Most personal, payroll and car loans are repaid with a fixed payment (also called the French amortization method): you pay the same amount every month, but what that payment is made of changes. At first almost all of it is interest; by the end, almost all of it is principal.

The formula is:

Payment = P × i ÷ (1 − (1 + i)⁻ⁿ)

where P is the amount borrowed, i is the rate per period (monthly, if you pay every month) and n is the number of payments.

Example: a $10,000,000 loan over 24 months at 1.5% per month has a payment of $499,241. You pay $11,981,784 in total, so the loan costs you $1,981,784 in interest.

Here's how the first payment breaks down:

On the second payment, interest is charged on the new, lower balance, so the principal portion grows a little. That repeats until the balance reaches zero on payment 24. That sequence is the amortization schedule, and the app builds the whole thing for you.

Nominal, effective annual and monthly rates: which is which

Two loans can both advertise "24%" and cost different amounts. It all depends on the type of rate:

• Monthly rate: what's charged each month on the balance. It's the one used in the payment formula.
• Effective annual rate (EAR): what the money really costs over a year, with interest compounded month by month. It's the best one for comparing loans.
• Nominal annual rate: the monthly rate times 12. It's easier to calculate, but it's always lower than the equivalent effective rate, so it makes a loan look cheaper.

To convert between them:

Monthly = (1 + EAR)^1/12 − 1   ·   EAR = (1 + monthly)¹² − 1   ·   Nominal annual = monthly × 12

The "24% nominal" loan ends up almost three points more expensive than the "24% effective" one. Before you sign, always ask for the effective annual rate. The app's rate converter shows every equivalent of a rate at once.

Extra payments: lower the payment or shorten the term?

An extra payment goes straight to reducing the balance, and since interest is charged on the balance, you always save. What changes is how much, depending on what you ask your lender for:

Example: with the same loan ($10,000,000, 24 months, 1.5% monthly), after 6 payments the balance is $7,824,385 and 18 payments remain, carrying $1,161,953 in interest. If you pay an extra $2,000,000 at that point:

Shortening the term saves more because the balance falls faster and accrues interest for less time. Lowering the payment is the right choice when what you need is breathing room in your monthly budget.

How to keep the books of a savings fund or group savings

In an informal fund, several members contribute money regularly and the fund lends to those same members at an interest rate. The numbers get tangled quickly, so it pays to track three things separately:

• Each member's contributions and withdrawals, with dates. A contribution recorded by mistake isn't deleted: it's voided, and the record stays.
• The fund's loans, each with its own amortization schedule and payments.
• The cash balance: what's available is what was contributed, minus what was lent, plus the principal, interest and fees collected so far.

In the app, the fund's administrator records contributions and loans, and each member sees the fund's total and their own contributions. It's a record-keeping tool: it doesn't move money. A formal employee savings fund may be a regulated entity and must follow the rules of its country.