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CS Professional · Banking and Insurance - Laws and Practice · Calculation of Interest and Annuities

Kavita Enterprises borrows from a bank and will repay by equal year-end instalments over 2 years at 10% p.a. compound interest. The present value annuity factor for 2 years at 10% is 1.7355. If the loan is Rs 8,677.50, which instalment amount is correct, and why?

The instalment is Rs 5,000 because an equal-instalment loan's amount equals the instalment times the present value annuity factor, so the instalment is the loan divided by 1.7355. Simply dividing by two ignores interest on the outstanding balance.

  1. ARs 4,338.75, being loan divided by number of years
  2. BRs 5,000, being loan divided by the annuity factorCorrect
  3. CRs 5,500, being loan multiplied by 1.1 and divided by 2
  4. DRs 4,000, being loan divided by the future value factor 2.1

Explanation

Instalment = Loan / PV annuity factor = 8,677.50 / 1.7355 = Rs 5,000. Check: 5,000/1.1 + 5,000/1.21 = 4,545.45 + 4,132.23 = 8,677.68, approximately the loan. Dividing by the number of years ignores interest on the outstanding balance.

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