Rest

Two loans can both say "12% a year" and "monthly EMI" and still cost different amounts. The difference is hidden in one word in the loan agreement: the rest.

Lenders use the term rest to indicate the interest charging cycle, which can be different from the payment cycle. A loan may be repaid every month while interest is calculated on the outstanding balance only once a year.

When that happens, the borrower's monthly payments do not reduce the balance on which interest is charged until the year ends. The workbook's conclusion: since the borrower is not getting credit for payments made during the year, the effective borrowing cost turns out to be higher than the interest rate quoted.

The workbook's method for a non-matching rest. Work out the repayment obligation first for the interest charging cycle, then divide it into instalments. With interest at 12% a year on annual rest:

1. Compute the annual instalment for the loan (period = 1 year).
2. For quarterly payments divide it by 4; for monthly payments divide by 12.

The workbook numbers. Its PMT illustration gives an annual instalment of Rs 27,740.97 for five years; the figures correspond to a Rs 1,00,000 loan at 12%. Monthly payment = 27,740.97 ÷ 12 = Rs 2,311.75, for 60 months.

If instead interest is 1% a month — a monthly rest — with the loan repaid over 5 years, the rate per period is 1% and there are 60 periods, and the EMI is Rs 2,224.44.

Same nominal 12%, same five years, same monthly payments — but the annual-rest borrower pays Rs 87.31 more every month, because eleven months' worth of payments sit with the lender without reducing the balance on which interest is charged.

Where rest also bites. In the workbook's criteria for evaluating loans, the reset period matters for floating rate loans too: a long reset period of, say, a year means the benefit of rate cuts reaches the borrower late — and, in a rising rate scenario, the higher rates also arrive later.

EMI = PMT(rate per period, number of periods, −loan)

Annual rest, monthly payment:
  Monthly payment = PMT(12%, 5, −1,00,000) ÷ 12 = 27,740.97 ÷ 12 = 2,311.75

Monthly rest:
  EMI = PMT(1%, 60, −1,00,000) = 2,224.44

Put the workbook's two figures side by side for a Rs 1,00,000 loan over five years at 12%:

The totals and the effective rate below are computed here from the workbook's EMIs.

Solving for the monthly rate that makes 60 payments of Rs 2,311.75 worth exactly Rs 1,00,000 today gives about 1.14% a month, roughly 14.6% a year compounded. The monthly-rest loan at 1% a month compounds to 12.7%. The "12%" on both loan documents conceals a gap of nearly two percentage points.

The workbook then uses the monthly-rest EMI to show debt servicing. A borrower earning Rs 10,000 a month with this as the only debt has a debt servicing ratio of 2,224.44 ÷ 10,000 = 22.24%. Extending the tenor to six years cuts the EMI to Rs 1,955.02 and the ratio to 19.55%; adding another loan with a Rs 1,000 monthly repayment takes total servicing to Rs 2,955.02 and the ratio to 29.55%.

For an adviser the practical lesson is one question to ask of every loan offer: what is the rest? A lower quoted rate on annual rest can cost more than a slightly higher quoted rate on monthly rest.

Chapter 4 (Debt Management and Loans), section 4.9 on loan calculations, where rest is defined and the EMI is computed with the PMT function; section 4.12(b) on reset periods as a criterion for evaluating loans. Expect a conceptual question — when rest is annual and payments monthly, is the effective cost higher or lower than the quoted rate (higher) — and PMT-based EMI arithmetic where rate and periods must be expressed per period.

• Rest is the interest charging cycle, not the payment cycle. They can differ.
• Annual rest with monthly payments raises the effective cost above the quoted rate, because payments during the year get no credit until year-end.
• Rate and periods must match the cycle. 1% a month means 60 periods over five years; 12% a year means 5 periods.
• Dividing an annual instalment by 12 is the workbook's method for annual rest, not a general EMI shortcut — for a monthly rest it gives the wrong, higher figure.
• A long reset period works both ways on floating loans: rate cuts reach the borrower late, and so do rate rises.