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1. Calculate the compound interest earned on each of the following. Give all answers correct to the nearest cent. ( i ). €800 invested for 3 years at 4% per annum. F = P (1 + i ) t. F = 800(1 + 0·04) 3. F = 800(1·04) 3 = €899·89. Interest earned = €899·89 – €800 = €99·89. (ii).

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  1. 1. Calculate the compound interest earned on each of the following. Give all answers correct to the nearest cent. (i) €800 invested for 3 years at 4% per annum. F = P(1 + i)t F = 800(1 + 0·04)3 F = 800(1·04)3 = €899·89 Interest earned = €899·89 – €800 = €99·89 (ii) €1,200 invested for 5 years at 3% per annum. F = P(1 + i)t F = 1200(1 + 0·03)5 F 1200(1·03)5 = €1391·13 Interest earned = €1391·13 – €1200 = €191·13

  2. 1. Calculate the compound interest earned on each of the following. Give all answers correct to the nearest cent. (iii) €9,000 invested for 4 years at 2·5% per annum F = P(1 + i)t F = 9000(1 + 0·025)4 F = 9000(1·025)4 = €9934·32 Interest earned = € 9934·32 – €9000 = € 934·32 (iv) €5,250 invested for 7 years at 3·8% per annum. F = P(1 + i)t F = 5250(1 + 0·038)7 F = 5250(1·038)7 = €6816·18 Interest earned = €6816·18 – €5250 = €1566·18

  3. 2. A sum of €6,000 is invested with an annual equivalent rate (AER) of 4·6%. Find the value of the investment when it matures in eight years’ time. Give your answer to the nearest cent. F = P(1 + i)t F = 6000(1 + 0·046)8 F = 6000(1·046)8 F = €8598·14

  4. 3. Which will earn more interest: €5,000 invested for 2 years at 3% per annum or €5,000 invested for 3 years at 2% per annum? Give your answer to the nearest cent. P = €5000, i= 3%, t = 2 P = €5000, i= 2%, t = 3 F = P(1 + i)t F = P(1 + i)t F = 5000(1 + 0·02)3 F = 5000(1 + 0·03)2 F = 5000(1·02)3 F = 5000(1·03)2 F = €5306·04 F = €5304·50 Therefore, 3 years at 2% yields more interest by €1·54

  5. 4. €8,500 is invested in a savings account where the interest is compounded annually with a rate of %. Calculate the future value of this investment in three and a half years. Give your answer to the nearest cent. P = €8500, i= 2·8%, t = 3·5 F = P(1 + i)t F = 8500(1 + 0·028)3·5 F = 8500(1·028)3·5 F = €9362·56

  6. 5. €4,600 is borrowed at a rate of 7% per annum. Find the value of the loan after 36 months. Give your answer to the nearest cent. 36  12 = 3 years P = €4600, i= 7%, t = 3 F = P(1 + i)t F = 4600(1 + 0·07)3 F = 4600(1·07)3 F = €5635·20

  7. 6. €15,000 is invested in a savings account where the interest is compounded annually with an AER of 3·5%. Calculate the future value of this investment in 51 months. Give your answer to the nearest cent. 51  12 = 4·25 years P = €15000, i= 3·5%, t = 4·25 F = P(1 + i)t F = 15000(1 + 0·035)4·25 F = 15000(1·035)4·25 F = €17361·52

  8. 7. €11,500 was invested for three years at compound interest. The rate for the first year was 1·5%, the rate for the second year was 2·2%, and the rate for the third year was 3%. Calculate the amount after three years, to the nearest cent. Year 1: P = €11500, i = 1·5%, t = 1 F = 11500(1 + 0·015) = 11500(1·015) = €11672·50 Year 2: P = €11672·50, i = 2·2%, t = 1 F = 11672·5(1 + 0·022) = 11672·5(1·022) = €11929·30 Year 3: P = €11929·30, i = 3%, t = 1 F = 11929·3(1 + 0·03) = 11929·3(1·03) = €12287·17 Final amount after the three years is €12,287·17

  9. 8. €22,000 was invested for four years at compound interest. The rate for the first year was 2·4%, the rate for the second year was 3%, and the rate for the third and fourth years was 4·6%. Calculate the amount after four years, to the nearest cent. Year 1: P = €22000, i = 2·4%, t = 1 F = 22000(1 + 0·024)1 = 22000(1·024) = €22528 Year 2: P = €22528, i = 3%, t = 1 F = 22528(1 + 0·03) = 22528(1·03) = €23203·84 Year 3+4: P = € €23203·84, i = 4·6%, t = 2 F = 23203·84(1 + 0·046)2 = 23203·84(1·046)2 = €25387·69 Final amount after the four years is €25,387·69

  10. 9. A woman borrowed €34,000 at 8% per annum compound interest. She agreed to repay €8,000 at the end of the first year, €10,000 at the end of the second year and wants to clear the debt at the end of the third year. How much was paid to clear the debt? Give your answer to the nearest cent. Year 1: P = €34000, i = 8%, t = 1 F = 34000(1 + 0·08)1 = 34000(1·08) = €36720 Repayment made: €36720 – €8000 = €28720 Year 2: P = €28720, i = 8%, t = 1 F = 28720(1 + 0·08)1 = 28720(1·08) = €31017·60 Repayment made: €31017·60 – €10000 = €21017·60 Year 3: P = €21017·60, i = 8%, t = 1 F = 21017·60(1 + 0·08)1 = 21017·6(1·08) = €22699·01 Therefore, €22699·01 needs to be paid, to clear the debt.

  11. 10. A man borrowed €15,000. He agreed to repay €2,500 after one year, €3,500 after two years and the balance at the end of the third year. If the interest was charged at 7·3% in the first year, 5% in the second year and 4·5% in the third year, how much was paid to clear the debt? Give your answer to the nearest cent. Year 1: P = €15000, i = 7·3%, t = 1 F = 15000(1 + 0·073)1 = 15000 (1·073) = €16095 Repayment made: €16095 – €2500 = €13595 Year 2: P = €13595, i = 5%, t = 1 F = 13595(1 + 0·05)1 = 13595(1·05) = €14274·75 Repayment made: €14274·75 – €3500 = €10774·75 Year 3: P = €10774·75, i = 4·5 %, t = 1 F = 10774·75(1 + 0·045)1 = 10774·75(1·045) = €11259·61 Therefore, = €11259·61 needs to be paid, to clear the debt.

  12. 11. What sum of money, to the nearest euro, will have a future value of €88,578·05 in 6 years at 10% per annum compound interest? F = € 88578·05, i = 10%, t = 6 F = P(1 + i)t 88578·05 = P(1 + 0·1)6 88578·05 = P(1·1)6 €50,000 = P

  13. 12. What sum of money, to the nearest euro, will have a future value of €4,116·69 in 4 years at 6·5% per annum compound interest? F = €4116·69, i = 6·5%, t = 4 F = P(1 + i)t 4116·69 = P(1 + 0·065)4 4116·69 = P(1·065)4 €3,200 = P

  14. 13. What sum of money, to the nearest euro, will have a future value of €2,036·53 in 5 years at 2·5% AER? F = €2036·53, i = 2·5%, t = 5 F = P(1 + i)t 2036·53 = P(1 + 0·025)5 2036·53 = P(1·025)5 €1,800 = P

  15. 14. How much should I invest, to the nearest euro, at 5% compound interest per annum, to have €8,000 in my account in 5 years time. F = €8000, i = 5%, t = 5 F = P(1 + i)t 8000 = P(1 + 0·05)5 8000 = P(1·05)5 €6268·21 = P €6268 = P

  16. 15. €15,500 was invested at a rate of r % per annum. If the future value of the investment in five years’ time was €21,236·34. Calculate the value of r, correct to one decimal place. F = €21236·34, P = €15500, t = 5 F = P(1 + i)t 21236·34 = 15500(1 + r)5

  17. 16. €8,000 was invested at a rate of r % per annum. If the future value of the investment in three years’ time was €8,741·82. Calculate the value of r. F = €8741·82, P = €8000, t = 3 F = P(1 + i)t 8741·82 = 8000(1 + r)3

  18. 17. An investment bond gives 25% interest at the end of 10 years. Calculate the AER for this bond. Give your answer to two decimal places. Based on an investment of €1: F = €1·25, P = €1, t = 10 F = P(1 + i)t

  19. 18. A savings account gives 21% interest at the end of 8 years. Calculate the AER for this savings account. Give your answer to two decimal places. Based on an investment of €1: F = €1·21, P = €1, t = 8 F = P(1 + i)t

  20. 19. Annette invested €P at r% compound interest per annum. After a year it amounts to €2,438. After two more years it amounts to €2,739·33. Find the values of r and P. Use the last two years to find the value of r: Use the value of r to find the value of P: F = € 2739·33, P = €2438, t = 2 F = € 2438, r = 6%, t = 1 F = P(1 + i)t 2739·33 = 2438(1 + r)2 2438 = P(1 + 0·06)1 €2300 = P 1·06 = 1 + r 0·06 = r 6% = r

  21. 20. €75,000 was invested for three years at compound interest. The rate for the first year was 3%. The rate for the second year was 2 %. At the end of the second year €10,681·25 was withdrawn. (i) Find the principal for the third year. Year 1: P = €75000, i= 3%, t = 1 F = 75000(1 + 0·03) = 75000(1·03) = €77250 Year 2: P = €77250, i= 2·5%, t = 1 F = 77250(1 + 0·025) = 77250(1·025) = €79181·25 Withdrawal: €79181·25 – €10681·25 = €68500

  22. 20. €75,000 was invested for three years at compound interest. The rate for the first year was 3%. The rate for the second year was 2 %. At the end of the second year €10,681·25 was withdrawn. (ii) The rate for the third year was r%. The total investment at the end of the third year was €70,897·50. Calculate the value of r correct to one decimal place. Year 3: F = €70,897·50, P = €68500, t = 1 F = P(1 + i)t 70897·50 = 68500(1 + r)1 1·035 = 1 + r 0·035 = r

  23. 21. A person invested €30,000 for three years at 5% AER. (i) Calculate the amount after two years. P = €30000, r = 5%, t = 2 F = P(1 + i)t F = 30000(1 + 0·05)2 F = 30000(1·05)2 F = €33075

  24. 21. A person invested €30,000 for three years at 5% AER. (ii) After two years a sum of money was withdrawn. The money which remained amounted to €26,250 at the end of the third year. Calculate the amount of money withdrawn after two years. Find the amount in the account at the start of the third year: F = €26250, r = 5%, t = 1 F = P(1 + i)t €25000 = P : sum in the account after the withdrawal Sum withdrawn = €33075 – €25000 = €8075 withdrawn

  25. 22. €45,000 was invested for three years at compound interest. Year 1: P = €45000, r = 6%, t = 1 F = 45000(1·06)1 = €47700 The AER for the first year was 6%, the AER for the second year was 4% and the AER for the third year was 3%. Withdrawal: €47700 – €7700 = €40000 Year 2: P = €40000, r = 4%, t = 1 F = 40000(1·04)1 = €41600 At the end of the first year €7,700 was withdrawn. Find principal for the third year: Year 3: F = €37080, r = 3%, t = 1 At the end of the second year € W was withdrawn. 37080 = P(1·03)1 At the end of the third year the investment was worth €37,080. €36000 = P Find the value of W. Sum withdrawn = €41600 – €36000 = €5600 withdrawn

  26. 23. €7,500 was invested for 2 years at r % per annum compound interest. (i) The amount of the investment at the end of the first year was €7,860. Find the value of r. F = €7860, P = €7500, t = 1 F = P(1 + i)t 7860 = 7500(1 + r)1 = 1 + r 1·048 = 1 + r 0·048 = r

  27. 23. €7,500 was invested for 2 years at % per annum compound interest. (ii) At the start of the second year €W was withdrawn from the account. The interest earned during the second year was €252. Find the value of W, to the nearest cent. Interest in 2nd year = €252 = 4·8% of principal for 2nd year €52·5 = 1% of P2 €5250 = 100% of P2 Amount withdrawn = Amount at end of 1st year – Principal at start of 2nd year w = €7860 – €5250 w = €2,610

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