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Arithmetic and Interest

This document provides a series of detailed examples for calculating compound interest on various principal amounts over different time periods and interest rates. It covers scenarios with different rates and offers step-by-step calculations for interest amounts on investments of €600, €1800, €3500, €7800, and €4600. The document also explains how to determine the total amount owed after repayments and investment returns over specified years. By following these examples, readers can enhance their understanding of compound interest and its applications in real-life financial situations.

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Arithmetic and Interest

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  1. Arithmetic and Interest

  2. Ex. 8A Q.1 (i) Calculate to the nearest cent where necessary the compound interest on (i) €600 for 2 years at 5% Year 1 P1 = €600 R1 = 5% A1 = ? I1 = ? Year 2 P2 = ? R2 = 5% A2 = ? I2 = ? €630 (600)(1.05) = €630 (630)(1.05) = €661.50 630 – 600 = €30 661.50 – 630 = €31.50 Compound Interest = 661.50 – 600 = €61.50

  3. Calculate to the nearest cent where necessary the compound interest on (ii) €1800 for 2 years at 9% Year 1 P1 = €1800 R1 = 9% A1 = ? Year 2 P2 = ? R2 = 9% A2 = ? €1962 (1800)(1.09) = €1962 (1962)(1.09) = €2138.58 Compound Interest = 2138.58 - 1800 = €338.58

  4. Ex. 8A Q.1 (iii) Calculate to the nearest cent where necessary the compound interest on (iii) €3500 for 3 years at 7½% P = €3500 R = 7½ % A1 = ? (3500)(1.075) = €3762.50 A2 = ? (3762.50)(1.075) = €4044.69 A3 = ? (4044.69)(1.075) = €4348.04 Compound Interest = 4348.04 - 3500 = €848.04

  5. Ex. 8A Q.1 (iv) Calculate to the nearest cent where necessary the compound interest on (iii) €7800 for 3 years at 3½% P = €7800 R = 3½ % A1 = ? (7800)(1.035) = €8073 A2 = ? (8073)(1.035) = €8355.56 A3 = ? (8355.56)(1.035) = €8648.00 Compound Interest = 8648 – 7800 = €848

  6. Ex. 8A Q.2 €4600 was invested for 2 years at compound interest. If the rate for the first year was 6% and for the second year was 9%, find the total interest for the two years. Year 1 P1 = €4600 R1 = 6% A1 = ? Year 2 P2 = ? R2 = 9% A2 = ? €4876 (4600)(1.06) = €4876 (4876)(1.09) = €5314.84 Compound Interest = 5314.84 – 4600 = €714.84

  7. Ex. 8A Q.3 A company borrowed €12000 from a bank at 11% per annum, compound interest. The company repaid €5000 at the end of the first year. How much was owed to the bank at the end of the second year. Year 1 P1 = €12000 R1 = 11% A1 = ? Year 2 P2 = ? R2 = 11% A2 = ? 13320 – 5000 = €8320 (12000)(1.11) = €13320 (8320)(1.11) = €9235.20 ANS: Amount owed = €9235.20

  8. Ex. 8A Q.4 €2500 was invested in a building society. If it amounted to €2612.50 after one year calculate the rate of interest? P = €2500 R = ? A = €2612.50 A/P = 2612.5/2500 = 1.045 Interest rate = 4½%

  9. Ex. 8A Q.5 A sum of money is invested at 7% p.a. if it amounts to €6848 after one year find the sum invested? P = ? R = 7% A = €6848 A = 107% P = 100% €6848 is 107% 6848/107 = €64 is 1% (64)(100) = €6400 is 100% ANS: P = €6400

  10. Income Tax Tax payable = Gross Tax – Tax credits

  11. Income Tax Questions can be done by filling in the following table

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