Partially Amortized Loan Calculator

Background.

Most home loans are paid down to nothing: every monthly instalment covers the interest and chips away at the principal until the last payment clears it. A partially amortized loan stops short. The payments repay only part of what was borrowed, and the remainder falls due in one lump, the balloon, when the regular payments end. Commercial property loans are often arranged this way, with payments sized as if the loan ran for 25 or 30 years while the loan itself ends after five or ten, and the same structure turns up in seller-financed property deals and some vehicle finance.

The attraction is a smaller monthly bill. On $200,000 at 7% over ten years, paying the loan off in full takes $2,322.17 a month; agreeing to leave $100,000 outstanding at the end cuts that to $1,744.42. The cost is twofold. More of the debt stays outstanding for longer, so more interest accrues over the term, and at the end you need to find the balloon, usually by refinancing or selling the asset. That lump sum is the risk the Consumer Financial Protection Bureau's guidance on balloon payments dwells on. If rates have risen, your income has fallen or the property is worth less by the time it arrives, refinancing may not be available on terms you can manage.

The structure suits a borrower who can see how the balloon will be met: a sale of the property already planned, cash a business expects to receive, or a refinance once the building's rental income has grown. It suits poorly anyone who would have to borrow again, on terms nobody can know yet, simply to keep what they bought.

The payment here assumes a fixed rate, compounded monthly, with equal payments at the end of each month. Fees, insurance, taxes and any change in rate are left out.

What is partially amortized loan calculator?

A partially amortized loan is a fixed-rate loan whose regular payments reduce the balance only partway, leaving a stated amount, the balloon, owed immediately after the last regular payment. The regular payment is the level monthly amount that exactly pays the interest each month and brings the balance down from the original principal to the balloon over the agreed number of payments. A balloon of zero is an ordinary fully amortizing loan; a balloon equal to the principal is an interest-only loan.

Lenders usually describe these loans with two periods rather than one. The amortization period is the notional schedule used to size the payment; the term, or maturity, is when the loan actually ends and whatever is left falls due. A loan written as a ten-year term on a 25-year amortization at 7% on $200,000 has a payment of $1,413.56 and leaves a balloon of about $157,266.79.

In every month the payment is split between interest on the current balance and a reduction of that balance. In the first month of the worked example, $1,166.67 of the $1,744.42 is interest and only $577.75 repays principal. Because the balance falls slowly, the interest portion stays large for longer than on a fully amortizing loan, which is where the extra cost of the structure comes from.

How to use this calculator.

1. 01Enter the principal, the amount actually borrowed after any deposit or down payment.
2. 02Enter the nominal annual rate from the loan offer as a percentage: the note rate in the contract, not the APR. It must be above zero; it is divided by 12 to get the monthly rate, and 0% finance is not handled.
3. 03Enter the number of monthly payments before the balloon falls due as a whole number: 60 for a five-year term, 120 for ten years.
4. 04Enter the balloon, the balance that will remain after the last regular payment. If your lender quotes a longer amortization period instead, the balloon is the balance that schedule would leave at the end of the term.
5. 05Read the monthly payment, then set it beside the balloon and ask how you would pay that lump sum when it arrives. Trying two or three balloon sizes side by side shows how much monthly relief each extra slice of deferred debt actually buys.

The formula.

PMT = [P − B ÷ (1 + r)ⁿ] × r ÷ [1 − (1 + r)⁻ⁿ], where P is the principal, B the balloon, n the number of monthly payments and r the monthly rate, the annual percentage divided by 1,200. The first bracket discounts the balloon back to today at the loan rate and subtracts it from the principal: that is the part of the loan the regular payments must clear. The second part is the standard annuity factor that turns a present amount into level monthly payments. A larger balloon shrinks the first bracket and therefore the payment.

The equation comes from following the balance. After k payments, the original debt has grown to P(1 + r)ᵏ, while the payments, each earning the loan rate from the month it is made, have paid off PMT × [(1 + r)ᵏ − 1] ÷ r. Set the balance after n payments equal to B and solve for PMT, and the formula above appears; multiplied through by (1 + r)ⁿ it can also be written PMT = [P(1 + r)ⁿ − B] × r ÷ [(1 + r)ⁿ − 1]. The same balance equation shows what an extra payment does: every additional dollar paid in month k cuts the balloon by that dollar grown at the loan rate to the end of the term, so an extra $100 a month on the example loan would shrink the $100,000 balloon by $17,308.48.

Three assumptions are built in. Payments fall at the end of each month, as on almost every loan; if each payment were due at the start of the month instead, it would be smaller by a factor of 1 + r, $1,734.30 rather than $1,744.42 in the example. The rate is nominal and compounds monthly, so a rate quoted as an effective annual yield must be converted first. And the rate is fixed for the whole term, while the rate on whatever refinances the balloon is unknown until it falls due. A balloon bigger than P × (1 + r)ⁿ, the balance the loan would reach with no payments at all, is rejected, since only a negative payment could produce it.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Kellison, Theory of Interest, 3rd ed. (PRINT).
2. [2]Consumer Financial Protection Bureau, Balloon loans.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.
4. [4]NIST Special Publication 811, Guide for the Use of the International System of Units, 2008 edition.
5. [5]Federal Reserve Regulation Z, 12 CFR Part 1026.