1. Useful Savings Facts & Formulae The amount invested is called the principal When a principal £ P earns compound interest at an annual rate R for n years, the final amount is: A = P (1 + R) n The annual rate at which a principal £P would increase to an amount £P in n years is: R =R = A P n – 1 AER = Interest earned in 1 year Amount at the beginning of the year  100% The AER corresponding to rate r added n times per year is: R = (1 + r) n – 1

2. A = P (1 + R) n Example A = 2000 (1 + 0.042 ) 10 = 2000 x 1.045 10 = 3017.916… Amount = £3017.92 (nearest pence) Neil invests £2000 at 4.2% per annum. Calculate the amount after 10 years. 4.2 100 R = = 0.042

3. The amount after n years is P = S  1.0035 12n Example a)P = 6000  1.0035 12 = 6256.908… Amount at the end of 1 year = £6256.91 (nearest pence) Kate invests £ S at 0.35% per month. a) Kate invests £6000. Find the amount at the end of 1 year. b) Hence find the AER. AER = 4.28% 256.91 6000 =  100% b) Interest earned in 1 year Amount at the beginning of the year AER =  100%

4. Annual % rate = 7.07% (to 3 sf) = 0.07071... An investment of £3500 has grown to £4600 in 4 years. Example R =R = A P n – 1 Find the annual percentage rate of interest. R = 4600 3500 4 – 1 = 1.31428... 4 – 1 = 1.07071... – 1