I buy a car from a dealership for £3500. The car depreciates in value for every year I own it. What is the value of the car after I have owned it for 18 months if it depreciates at a rate of 5 percent?
This is a compound interest problem. Here we have to put 18 months in terms of years. There are 12 months in a year, so 18 months is a year and 6 months.
6 months is half a year, so 18 months represents a year and a half (1.5)
The rest is a compound interest problem. as a decimal, 5% represents 0.05, and since the car depreciates in value, we minus this from 1 to get 0.95. Essentially what we do is repeatedly multiply the number by 0.95 for the amount of years we own the car, and this means putting the number to the power of the amount of years owned. This means that the value of the car after 1.5 years would be
3500 x 0.951.5 = 3240.81 (2 d.p since money only goes to 2 d.p)
You can remember this structure
1.) Put the percentage into decimal form2.) Add this percentage on to 1 for an appreciation (increase) or minus is from one for a depreciation (decrease)3.) Put this number to the power of the amount of time the object/investment is owned (the amount of time mentioned in the question). Be careful to be consisteent with the measurement of time mentioned in the question. This may be converting between months/year, or days/hours. 4.) Multiply this number by the original value.
