Deferred Payment Loan Calculator

Background.

Putting off a loan's payments does not put off its interest. Unless a lender or a government agrees to cover it, interest keeps accruing through a grace period, a payment holiday or the years of a degree, and the balance you start repaying can be noticeably larger than the amount you borrowed.

How much larger depends on four things: the amount owed when the deferral begins, the annual rate, how long the deferral lasts, and whether unpaid interest is folded into the balance as it goes — so that next month's interest is charged on this month's interest too. This page assumes it is, at a regular frequency you choose. Defer $10,000 at 8% compounded monthly for four years and you owe $13,756.66 before the first payment is due. Had the same interest accrued simply, without compounding, the figure would be $13,200; the extra $556.66 is interest on interest.

That contrast matters because real loans differ. Many student loans charge simple daily interest during deferment and add the unpaid total to the principal only at specific events, such as the end of the deferment; subsidised loans may charge the borrower nothing while an eligible deferment lasts. For loans like these, read the compounded figure as an upper estimate and take the actual terms — capitalisation dates, day counts, fees — from the agreement.

Where the model does fit, a balance left to compound untouched, it answers the planning question directly: subtract the principal from the result and you have the price of not paying, in the loan's own currency.

What is deferred payment loan calculator?

The balance after deferral is what the borrower owes at the moment payments resume, assuming nothing was paid in the meantime and unpaid interest was compounded into the balance at regular intervals. It equals the starting principal plus every unit of interest accrued during the deferral, including interest charged on earlier interest. It is expressed in the same currency as the principal, and the gap between the two is the cost of deferring.

How to use this calculator.

1. 01Enter the principal: the amount borrowed, or the balance outstanding when the deferral starts if part of the loan has already been repaid. Any currency works; the balance comes back in the same one.
2. 02Enter the nominal annual rate as a percentage — the yearly interest rate stated in the agreement, not a monthly rate. Rates above zero and up to 1,000% are accepted.
3. 03Enter how many times a year unpaid interest is added to the balance: 12 for monthly, 4 for quarterly, 365 for daily. If the agreement says interest is simple and capitalised once, expect this model to run slightly high.
4. 04Enter the deferral length in years, with decimals for part-years: 6 months is 0.5, 18 months is 1.5. Up to 100 years is accepted.
5. 05Read the balance after deferral, then subtract the principal to see how much interest the deferral adds.

The formula.

B = P(1 + r/m)^(m·t). P is the principal, r the nominal annual rate as a decimal (8% is 0.08), m the number of compounding periods per year and t the deferral in years. Each period the balance is multiplied by 1 + r/m — at 8% compounded monthly, by 1.0066667 — and m·t counts how many times that happens. The rate and the length of the deferral move the answer far more than the compounding frequency: at 8% for one year, switching from annual to daily compounding lifts $10,000 only from $10,800 to $10,832.78, while stretching a monthly-compounded deferral from one year to four lifts it from $10,830.00 to $13,756.66. Neither m nor t has to be a whole number. The formula assumes no payments at all during the deferral and charges no fees.

A worked example.

Frequently asked questions.

References& sources.

1. [1]U.S. Federal Reserve, Regulation Z, Appendix J — Annual Percentage Rate Computations.
2. [2]OpenStax, Principles of Finance, Time Value of Money.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.