Whiteboardmaths.com © 2007 All rights reserved

Intro Compound Interest Suppose £100 is invested in a building society at a rate of 10% per annum. At the end of the year the interest paid would be £10 and if this is withdrawn, leaving the original £100 in the account for a further year at 10% then this type of interest is called simple interest. £33.10£30.00Total Interest gained £133.10£130Amount after 3years £121£120Amount after 2 years £110 Amount after 1 year Compound InterestSimple Interest The table below shows how £100 grows over a 3 year period if it is invested at a rate of 10% If the annual interest is left in the account at the end of each year then the interest is called compound interest.

Worked Example 1 £2000 is invested at 6% compound interest for 3 years. Find: (a) the amount in the account at the end of the period. and (b) the interest accrued. Amount after 1 year = % of 2000 = = £2120 Amount after 2 years = % of 2120 = = £ Amount after 3 years = % of = = £ Interest accrued = £ – £2000 = £ Long Method Compound Interest Long Method

Question 1 £600 is invested at 5% compound interest for 3 years. Find: (a) the amount in the account at the end of the period. and (b) the interest accrued. Amount after 1 year = % of 600 = = £630 Amount after 2 years = % of 630 = = £ Amount after 3 years = % of = = £ Interest accrued = £ – £600 = £94.58 Long Method Compound Interest

Question 2 £5000 is invested at 8% compound interest for 4 years. Find: (a) the amount in the account at the end of the period (nearest £). and (b) the interest accrued (nearest £). Amount after 1 year = % of 5000 = = £5400 Amount after 2 years = % of 5400 = = £5832 Amount after 3 years = % of 5832 = £ = £ Interest accrued = £6802 – £5000 = £1802 Amount after 4 years = % of = = £6802 Long Method Compound Interest

Tricky Question £3000 is invested at 7% compound interest for 15 years. Find: (a) the amount in the account at the end of the period (nearest £). and (b) the interest accrued (nearest £). What problems would you have with the following question using this method? Long Method We can avoid 15 calculations by considering a different approach to the problem to devise a more efficient method. We will rework Example Question 1(a) using this improved method. Compound Interest

Multiplicative Remember that 6% means = 0.06 At the end of each year the money grows to 106% of its value at the start of the year = = 1.06 After 1 year the money has been multiplied by 1.06  2000 x 1.06 After 2 years the money is again multiplied by 1.06  (2000 x 1.06) x 1.06 After 3 years the money is again multiplied by 1.06  (2000 x 1.06 x 1.06) x 1.06 So after 3 years the money will have grown to £2000 x Worked Example 1 £2000 is invested at 6% compound interest for 3 years. Find: (a) the amount in the account at the end of the period. Efficient Method (a) Money at end of 3 years = 2000 x = £ Explanation of the Method If the term had been 7 years and the interest rate 8% then we would simply have calculated 2000 x Compound Interest

Question 1 £600 is invested at 5% compound interest for 3 years. Find: (a) the amount in the account at the end of the period. and (b) the interest accrued. Amount after 1 year = % of 600 = = £630 Amount after 2 years = % of 630 = = £ Amount after 3 years = % of = = £ Interest accrued = £ – £600 = £94.58 Long Method Use this efficient method to confirm the answer to Question 1 (a) below Amount after 3 years = 600 x = £ Compound Interest

Question 2 £5000 is invested at 8% compound interest for 4 years. Find: (a) the amount in the account at the end of the period (nearest £) and (b) the interest accrued (nearest £) Amount after 1 year = % of 5000 = = £5400 Amount after 2 years = % of 5400 = = £5832 Amount after 3 years = % of 5832 = £ = £ Interest accrued = £6802 – £5000 = £1802 Amount after 4 years = % of = = £6802 Long Method Use this efficient method to confirm the answer to Question 2 (a) below Amount after 4 years = 5000 x = £6802 Compound Interest

Question 3 £8000 is invested at 7% compound interest for 6 years. Find: (a) the amount in the account at the end of the period (nearest £) and (b) the interest accrued (nearest £) Question 4 £1250 is invested at 9% compound interest for 10 years. Find: (a) the amount in the account at the end of the period (nearest £) and (b) the interest accrued (nearest £) (a) 8000 x = £12,006 (b) 12,006 – 8000 = £4,006 (a) 1250 x = £2959 (b) 2959 – 1250 = £1709 Compound Interest

Question 5 £3750 is invested at 4.5% compound interest for 8 years. Find the amount in the account at the end of the period (nearest £100) Question 6 £7500 is invested at 8.5% compound interest for 15 years. Find the amount in the account at the end of the period (nearest £100) Answer: 3750 x = £5300 Answer: 7500 x = £ Compound Interest

Worksheets Q1. £600 is invested at 5% compound interest for 3 years. Find: (a) the amount in the account at the end of the period. and (b) the interest accrued. Q2. £5000 is invested at 8% compound interest for 4 years. Find: (a) the amount in the account at the end of the period (nearest £) and (b) the interest accrued (nearest £) Worked Example 1: £2000 is invested at 6% compound interest for 3 years. Find: (a) the amount in the account at the end of the period and (b) the interest accrued. Worksheet 1

Q3. £8000 is invested at 7% compound interest for 6 years. Find: (a) the amount in the account at the end of the period (nearest £) and (b) the interest accrued (nearest £) Q4. £1250 is invested at 9% compound interest for 10 years. Find: (a) the amount in the account at the end of the period (nearest £) and (b) the interest accrued (nearest £) Q5.£3750 is invested at 4.5% compound interest for 8 years. Find the amount in the account at the end of the period (nearest £100) Q6. £7500 is invested at 8.5% compound interest for 15 years. Find the amount in the account at the end of the period (nearest £100) Worksheet 2