What are the decimal multipliers for these changes: a) value increasing by 4% for one year b) value increasing by 4% for four years c) value depreciating by 8% for six years

Question

Please can this be explained in a way that I can understand the method.

Answer 1

You're looking at the growth rate or depreciation rate as well as the number of years.

For the first one it's only one year so it's just 1.04 times the original number to get an answer that's 4% higher. So the decimal multiplier is 1.04.

When there are multiple years you have to raise your multiplier to the power of X where X is the number of years. For the second answer you would calculate 1.04 to the fourth power as your multiplier. An easier way to think about it (but more tedious math) is 1.04 * 1.04 * 1.04 * 1.04 = 1.1699

With depreciation the concept is the same but you want a smaller number in the end. 8% depreciation is the same as multiplying by (1 - .08) or .92. So .92 to the eighth power would be your multiplier. Same as above it's like saying (.92 * .92 * .92 * .92 * .92 * .92 * .92 * .92) = .5132