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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)

A borrower takes a loan of ₹1,00,000 at 8% p.a. effective. She pays ₹30,000 at the end of year 1 and ₹40,000 at the end of year 2. The loan is cleared by a single final payment at the end of year 3. What is that final payment?

The final payment is ₹47,779.20. Roll the balance forward year by year: ₹78,000 after the first payment, then ₹44,240 after the second. Accumulating ₹44,240 for one more year at 8% gives the amount needed to clear the loan.

  1. A₹44,240.00
  2. B₹47,779.20Correct
  3. C₹54,000.00
  4. D₹55,971.20
  5. ₹30,000.00

Explanation

Balance after year 1: 1,00,000 × 1.08 − 30,000 = 78,000. Balance after year 2: 78,000 × 1.08 − 40,000 = 44,240. The final payment is 44,240 × 1.08 = 47,779.20. The figure ₹55,971.20 comes from accumulating the loan for 3 years and deducting the payments without accumulating them.

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