Skip to content

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

A loan of Rs 1,000 is repaid by two monthly instalments: Rs 510 at the end of month 1 and Rs 520.20 at the end of month 2. The APR is the effective annual rate equivalent to the monthly rate implied by the loan. What is it, to two decimal places?

The APR is 26.82%. The monthly rate that equates the two instalments to Rs 1,000 is 2%, since each instalment discounts to Rs 500. Compounding 2% over twelve months gives 1.02^12 - 1, about 26.82% effective annual.

  1. A12.62%
  2. B24.00%
  3. C26.00%
  4. D26.82%Correct
  5. 27.12%

Explanation

Try a monthly rate j = 2%. Then 510/1.02 + 520.20/1.0404 = 500 + 500 = 1,000, so j = 2%. The APR is 1.02^12 - 1 = 1.268242 - 1 = 26.82%. The 24.00% option is 12 x 2%, the nominal rate. The 12.62% option treats 2% as a two-month rate. The 27.12% option uses continuous compounding, e^0.24 - 1.

Did you get it right without looking?

One question tells you little. A timed set on Practical applications of the equation of value (loans and APR) shows your real accuracy, how long you take and where you lose marks.

Practise Practical applications of the equation of value (loans and APR)Free diagnostic mock

More Practical applications of the equation of value (loans and APR) questions