Problem 62 in the OG describes someone who has invested $10,000 three years ago. The value increases 10% the first year, increases 5% the second year, and decreases 10% the third year. We are to determine the value of the account today.
When I first did this problem, I used the simple interest formula for each year, using the previous year's total as the new principle and came out with the correct answer of $10,395.
However, the answer in the book says that the first year's increase can be expressed as 1.10, the second increase by 1.05, and third decrease by 0.90. Then the answer multiplies them all together:
10,000(1.10)(1.05)(0.90) = 10,395.
My question is how do they just know that 10% increase can be expressed by 1.10, the 5% by 1.05, and the 10% decrease by 0.90? I can see how the calculation works, and I can even interpret that they are adding or subtracting the percentages from 100%, but where did formula come from? How is it derived?
I'd like to see all of the steps in how and why 10% increase can be expressed by 1.10, etc. because something just isn't registering completely in my mind about it.
When I first did this problem, I used the simple interest formula for each year, using the previous year's total as the new principle and came out with the correct answer of $10,395.
However, the answer in the book says that the first year's increase can be expressed as 1.10, the second increase by 1.05, and third decrease by 0.90. Then the answer multiplies them all together:
10,000(1.10)(1.05)(0.90) = 10,395.
My question is how do they just know that 10% increase can be expressed by 1.10, the 5% by 1.05, and the 10% decrease by 0.90? I can see how the calculation works, and I can even interpret that they are adding or subtracting the percentages from 100%, but where did formula come from? How is it derived?
I'd like to see all of the steps in how and why 10% increase can be expressed by 1.10, etc. because something just isn't registering completely in my mind about it.
