Solve for Rate, Term, Loan Amount or Payment From the Other Three

A dealer offers you $18,000 to be repaid at $350 a month for 60 months. The quote lists the payment and the term but no interest rate. Over five years you would pay $21,000 in total, so the loan costs $3,000 — but what rate is that?

It works out to 6.24% a year. You don't need a spreadsheet for this. A standard loan with equal monthly payments ties together exactly four numbers: the amount, the rate, the term and the payment. Know any three and the fourth is fixed. Loan Calculator's Solve for any variable tool finds it for you.

What should you compare?

Every question in this guide is one of these four numbers, seen from a different side:

• Amount — how much you borrow. Solve for it when you know what you can pay each month.
• Rate — the annual interest rate. Solve for it when a quote gives you the payment but not the rate.
• Term — how many months until the loan is paid off. Solve for it when you have a fixed amount you can put toward a debt.
• Monthly payment — what you pay each month. Solve for it to check a quote or test a loan before you apply.

The four solves at a glance

Each row leaves a different field empty. Figures use the equal-payment (reducing-balance) method, the only one the tool solves.

1. Solve for the monthly payment

Best for: checking a quote, or seeing what a loan costs each month before you apply.

This is the classic loan formula. With the monthly rate r (annual rate ÷ 12) and n months:

Payment = P × r ÷ (1 − (1 + r)^−n)
r = 6.5% ÷ 12 = 0.541667% a month
Payment = $300,000 over 360 months ≈ $1,896.20

Of that first payment, $1,625.00 is interest, because the whole $300,000 is still outstanding. Over the full 30 years the interest adds up to $382,636.71.

The main calculator gives you the same payment along with the full schedule. The solve dialog is quicker when you only want the number, and it becomes much more useful when you turn the question around.

2. Solve for the loan amount

Best for: turning a monthly budget into a borrowing limit.

Leave Amount empty and type what you can pay each month:

Amount = Payment × (1 − (1 + r)^−n) ÷ r
$2,000 a month, 6.5%, 360 months → $316,421.64

The answer shows how sensitive borrowing power is to the rate and term:

• At 7.5% instead of 6.5%, the same $2,000 supports only $286,035.25 — $30,386.39 less for one percentage point.
• At 6.5% over 240 months instead of 360, it supports $268,250.01.

3. Solve for the term

Best for: finding out when a debt will be gone if you pay a fixed amount.

Leave Term (months) empty. For $25,000 at 7.5% paying $500 a month, the exact answer is about 60.1 months. Loans are paid in whole months, so the app returns the shortest whole number of months whose payment is not above what you entered:

Why 61 and not 60? Over 60 months the payment would be $500.95 — more than the $500 you said you can pay. Over 61 months it is $494.18, which fits.

When there is no term

Every month, interest is charged on the balance first. If your payment does not cover that interest, the balance never goes down. For $300,000 at 6.5%, the first month's interest is $1,625.00:

• Paying $1,600, or even exactly $1,625, gives No solution with these numbers.
• Paying $1,650 — only $25 above the interest — gives 776 months, which is 64 years and 8 months.

The tool also reports no solution when the answer would be longer than 1,200 months (100 years).

4. Solve for the rate

Best for: finding the rate inside a quote that only states a payment.

Leave Rate (%/year) empty. There is no neat formula for the rate, so the app searches for the rate that produces your payment and rounds it to two decimals. For the $18,000 loan at $350 a month over 60 months, the answer is 6.24, and a 6.24% loan does come to $350.00 a month.

Decode a flat-rate quote

Some loans are quoted at a "flat" rate, where interest is charged on the original amount for the whole term. Take $12,000 at 8% flat for 36 months:

Principal per month = 12,000 ÷ 36 = 333.33
Interest per month  = 12,000 × 8% ÷ 12 = 80.00
Payment             = $413.33

Enter $12,000, 36 months and $413.33, leave the rate empty, and the answer is 14.55%. That is the reducing-balance rate that gives the same payment. A true 8% reducing-balance loan would cost $376.04 a month and $1,537.31 in interest, compared with $2,880.00 for the flat quote. The flat rate vs reducing balance guide explains why the gap is so large.

When there is no rate

Even at 0% you would have to repay the amount divided by the number of months. For $18,000 over 60 months that is $300.00, so:

• a payment of $300 gives a rate of 0;
• a payment of $290 gives No solution with these numbers.

5. How to use Solve for any variable in Loan Calculator

Best for: answering "what if" questions in seconds, without touching the loan you have already calculated.

1. Open the Tools tab and tap Solve for any variable. After you calculate a loan, the same tool also appears as a chip under the results.
2. The dialog has four fields: Amount, Rate (%/year), Term (months) and Monthly payment. They start empty; nothing is copied from the main form.
3. Fill in exactly three and leave the one you want to find empty. Enter the term in months, so a 30-year loan is 360.
4. Tap Solve. The answer appears in the empty field. Amounts are rounded to cents and the rate to two decimals.
5. If you leave no field empty, or more than one, you will see "Leave exactly one field empty and fill the other three."
6. The dialog stays open after each answer. Clear a different field and tap Solve again to ask the next question. Tap Cancel when you are done.
7. To see the full amortization schedule for an answer, enter the numbers in the main calculator and tap Calculate.

Which value should you solve for?

FAQ

Why is the solved term longer than I expected?

The app only returns whole months, and it picks the shortest term whose payment does not exceed yours. If the exact answer is 60.1 months, you get 61, because 60 months would need a slightly higher payment.

Does Solve work for equal principal or flat-rate loans?

No. It uses the equal-payment method, as the note at the top of the dialog says. With equal principal, the payment changes every month, so there is no single payment to solve for. For a flat-rate quote, work out the payment first and then solve for the rate, as shown above.

Why does the solved rate have only two decimals?

The rate field works like the rest of the app: two decimals are enough to compare quotes. A rate rounded to two decimals can be off by a few cents a month from the exact payment, which does not change any decision.

What does "No solution with these numbers" mean?

The three numbers you entered cannot belong to the same loan. Usually the payment is too small: it does not cover the first month's interest (when solving for the term) or is less than amount ÷ term (when solving for the rate).

Does the app work offline?

Yes. Every solve runs on your device and works with no internet connection. The numbers you type stay on your phone.