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Annuities, sinking funds and loan instalments sheet
Essay frame

A Rs. 331,000 loan at 10% a year is repaid by 3 equal instalments at the end of each year. (a) Find the instalment. (b) Prepare the repayment schedule. (c) Find the total interest.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Choose the formula. The loan is the present value of the instalments: R = A × i ÷ [1 − (1 + i)^(−n)].
  2. 2 · Substitute. R = 331,000 × 0.1 ÷ (1 − 1/1.331) = 33,100 × 1.331 ÷ 0.331 = Rs. 133,100.
  3. 3 · Draw the schedule. [Table: Year | Opening | Interest | Instalment | Principal | Closing]
  4. 4 · Fill each row.
    • Y1: 331,000 | 33,100 | 133,100 | 100,000 | 231,000
    • Y2: 231,000 | 23,100 | 133,100 | 110,000 | 121,000
    • Y3: 121,000 | 12,100 | 133,100 | 121,000 | 0
  5. 5 · Total interest. 3 × 133,100 − 331,000 = Rs. 68,300 (= 33,100 + 23,100 + 12,100).
  6. 6 · Business link. Leasing companies give exactly this schedule; the interest share falls each year.