John invests £8000 at compound interest rate of 1.5% per year. He wants to earn more than £2000 in interest. What is the LEAST time in WHOLE years that this will take?
Step 1) Create the formula: 8000 x 1.015nStep 2) Equate to the target value: 8000 x 1.015n = 2000 10000 (Common mistake is to use target of £2000 but you must also take into account the £8000 that is already in the account as this is what will determine the amount of interest John gets per year)Step 3) Re-arrange to get value with 'n' by itself: 1.015n = 5/4Step 4) Use logs to find an exact value for n: Log1.015(1.015n) = Log1.015(5/4) => (Logs in first part of equation cancel) n = 14.988LEAST amount of WHOLE years = 15 (Always round up as if we rounded down the interest earned would be <£2000)
