What a repayment actually does, and why the balance falls so slowly at the start.
200,000 borrowed at 6% a year, repaid monthly over 25 years. The payment is the same 1288.60 every month. Run the payments and watch what it is spent on.
The payment never changes. What it buys does.
Each month, interest is charged on what is still owed, and whatever is left of your payment comes off the debt. Early on the debt is huge, so the interest is huge and almost nothing comes off. As the balance falls, the interest falls with it and the payment starts to bite.
Half the term is not half the debt. After 150 payments of 300 you still owe 135,754 of the 200,000. The total repaid over 25 years is about 386,580, so the interest alone is 186,580, nearly the size of the loan itself.
A loan is a lump sum now, paid off by instalments. An annuity is instalments now, bought with a lump sum. Same formula, same calculator screen, and the only thing that changes is which quantity you are solving for. In the finance solver, money coming to you and money going from you must have opposite signs, which is the single commonest reason an answer comes out negative or absurd.
| Field | Means | Here |
|---|---|---|
| N | number of payments | 300 |
| I% | annual rate | 6 |
| PV | present value | 200000 |
| PMT | payment | −1288.60 |
| FV | future value | 0 |
| P/Y, C/Y | payments and compounds a year | 12, 12 |
N is the number of payments, not the number of years. 25 years paid monthly is N = 300. Putting 25 in N with P/Y = 12 is the error that produces a wildly wrong payment and still looks like a number.
A graduate borrows 400,000 baht for a car at 7% a year, repaid monthly over 5 years.
Find the monthly payment, the total interest, and how much of payment 1 actually reduces the debt.
1. 200,000 at 6% a year, monthly. Find the interest in the first payment.
2. A loan repaid monthly over 25 years. State N.
3. After 150 of the 300 payments, the amount still owed is:
N as the number of payments, and the rate matched to the payment period.
Consistent signs in the finance solver, so money in and money out differ.
Answering the question asked: total interest is total paid minus the amount borrowed, which is two steps, not one.
These three are deliberately not all about this page. In an examination the hardest step is deciding which method applies, and questions that arrive straight after the method never make you decide. Answer from memory before you reveal anything.
Come back to these in a week, and again in a month.
Which method?
A ball bounces for ever, rebounding to 0.8 each time. Does it travel a finite distance?
Which method?
Find the modulus of 3 + 4i.
Which method?
200000 at 6% a year, monthly, over 25 years. How many payments?
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