Introduction: This topic is very practical and appears frequently in Paper I and Paper II. Master the difference between reducing balance and compound interest. The "month units" formula is a huge time-saver for reducing balance questions.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Define): What is the main difference between simple interest and compound interest?

• Prompt 2 (Define): What is meant by "reducing balance" when calculating interest for a loan?

• Prompt 3 (Calculate): A loan of Rs. 24,000 is to be paid in 12 equal monthly installments. What is the value of the principal paid each month?

• Prompt 4 (Formula): Write down the formula to calculate the number of "month units" for a loan paid in 'n' installments.

• Prompt 5 (Calculate): Calculate the compound interest for Rs. 10,000 for 2 years at an annual interest rate of 10%.

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Problem Solve): A loan of Rs. 50,000 is repaid in 10 equal monthly installments. The annual interest rate is 12% on the reducing balance. Calculate the total interest paid.

• Prompt 2 (Problem Solve): Using the information from the previous prompt, calculate the value of a single monthly installment.

• Prompt 3 (Problem Solve): A person deposits Rs. 80,000 in a bank that pays 8% annual interest compounded semi-annually. What is the total amount in the account after one year?

• Prompt 4 (Working Backwards): A TV worth Rs. 35,000 is bought with a down payment of Rs. 5,000. The rest is paid in 15 monthly installments of Rs. 2,240. Find the total interest paid.

• Prompt 5 (Working Backwards): Using the information from the previous prompt, find the annual interest rate charged on the reducing balance.

  
  

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Compare): Nimal takes a loan of Rs. 120,000 for 2 years at 10% annual simple interest. Sunitha takes the same amount for the same period at 9% annual compound interest. Who pays more interest in total and by how much?

• Prompt 2 (Problem Solve): A motorcycle is priced at Rs. 180,000. It can be bought with a down payment of Rs. 30,000 and the rest paid in 2 years with 24% annual interest on the reducing balance. Find the value of a monthly installment.

• Prompt 3 (Explain): Explain why, for a borrower, the reducing balance method is more advantageous than paying simple interest on the full loan amount over the entire period.

• Prompt 4 (Problem Solve): The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 420. Find the principal amount.

• Prompt 5 (Application): A refrigerator worth Rs. 70,000 can be bought with a down payment of 20% and the remainder paid in 20 monthly installments. If the annual interest rate on the reducing balance is 15%, calculate the value of an installment.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Challenge): A person borrows a certain amount at 8% per annum compound interest. He repays the entire loan by paying Rs. 14,580 at the end of 2 years. What was the original amount he borrowed?

• Prompt 2 (Multi-step): A housing loan of Rs. 1,200,000 is given at an annual interest rate of 6% on the reducing balance, to be paid over 10 years (120 months). Calculate the value of a monthly installment.

• Prompt 3 (Derive): A loan is taken for 'n' months at an annual interest rate of 'r'% on the reducing balance. If the loan amount is 'L', derive a single formula for the value of one monthly installment in terms of L, n, and r.

• Prompt 4 (Synthesis): A sum of money amounts to Rs. 4,840 in 2 years and to Rs. 5,324 in 3 years on compound interest. Find the rate of interest and the principal sum.

• Prompt 5 (Analysis): Two loan schemes are offered for Rs. 60,000 for one year. Scheme A: 15% annual simple interest. Scheme B: 18% annual interest on the reducing balance, paid in 12 monthly installments. By calculating the total amount repayable under each scheme, determine which scheme is better for the borrower and by how much.