Compound Interest When we save with a bank the bank pays us interest at the end of each year. If we leave the money alone then the interest gets added to our balance giving us a bigger balance. The next time we calculate the interest it is a % of a larger sum than before. Example Suppose we put £ 500 into an account which pays a rate of 4% per annum. How much is this worth after 3 years? How much interest do we get for the 3 years?
Long Method 4% = 0. 04 Int in year 1 = 0. 04 X £ 500 = £ 20 Balance after 1 st year = £ 520 Int in year 2 = 0. 04 X £ 520 = £ 20. 80 Balance after 2 nd year = £ 540. 80 Int in year 3 = 0. 04 X £ 540. 80 = £ 21. 632 = £ 21. 63 Balance after 3 rd year = £ 562. 43 Interest gained in 3 years = £ 562. 43 - £ 500 = £ 62. 43
Quick Method Adding 4% gives us 104% or 1. 04 so Balance after year 1 = 1. 04 X £ 500 = £ 520 Balance after year 2 = 1. 04 X £ 520 = £ 540. 80 Balance after year 3 = 1. 04 X £ 540. 80 = £ 562. 432 = £ 562. 43 Again total interest = £ 62. 43
Really Quick Method Adding 4% gives us 104% or 1. 04 We multiply by 1. 04 on three occasions so Balance after year 3 = 1. 04 X £ 500 = (1. 04)3 X £ 500 = £ 562. 432 = £ 562. 43 Again total interest = £ 62. 43 Use the xy button
APPRECIATION - Growing in value. Example When it is growing a baby shark’s weight increases by 18% per week. If a baby shark is currently 40 kg then how heavy will it be in 5 weeks time ? (to the nearest kg) ********* 18% more gives us 118% or 1. 18 Weight in 5 weeks =1. 18 X 40 kg = 91. 51…kg = 92 kg
DEPRECIATION - Loss of value. Example For each km you climb a mountain the amount of oxygen in the air becomes 13% less. The air at ground level contains 20 units of oxygen. How many units will there be at the top of Mount Everest which is 8 km high? ********* 13% less gives us 87% or 0. 87. Oxygen level = 0. 87 X 0. 87 X 20 units = 6. 56 units Hence need for masks!!
Example The Simpsons buy a house for £ 80000. The following year it is worth £ 84000. What is the rate of appreciation? ****** Actual increase = £ 84000 - £ 80000 = £ 4000 % increase = 4000 80000 = 0. 05 or 5%
Example On its first bounce a pogo stick reaches a height of 48 cm. On its second bounce it only reaches a height of 42 cm. What is the % depreciation in height? ******* Actual change = 48 – 42 = 6 % change = 6 48 = 0. 125 or 12. 5%
Example A car completes one lap of a track at 87 mph. It then completes a second lap at 78 mph. Find the % drop in speed! ******* Actual drop = 87 - 78 = 9 mph % drop = 9 87 = 0. 1034…. . = 0. 103 = 10. 3%
Example The population of town is 36000. This is expected to rise by 8% per annum over the next five years. ****** 8% more = 108% or 1. 08 Pop in 5 years = 36000 X 1. 08 OR = 36000 X (1. 08)5 = 52895. 8. . . = 52900 To nearest 100.
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