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- Sven Smorgasbord is 35 years old is presently experiencing the “good” life. As a result, he anticipates that he will increase his weight at a rate of 3 percent a year. At present he weighs 200 pounds. What will he weigh at age 60?
- The answer is 418.76 pounds.
Ok. This is a 'fairly' simple growth question. The formula I'm using is for compound growth which I'm sure you've heard of, as you put this question in the right section. (Compound growth is used most in finance). This is how the formula looks:
FV = PV ( 1+i )^n
Where FV is future value (his future weight which is what you want). 'i' is the growth rate. 3% growth means i will be 0.03. And n is the number of years he'll grow over, which is 60-35 = 25 years old. For this question the formula could be worded as:
Weight, multiplied by ((1+percentage growth) to the power of number of years he'll be growing).
The answer is 418.76 pounds.
To help you understand. If you're growing by 3 percent a year. then next year you will be 1.03 multiplied by the weight you are now. This would be 200 * 1.03
His weight in two years would be 200 * 1.03 (the weight after the first year) which will then grow by 1.03, so the above bit needs to be multiplied by another 1.03. So in two years he'll be 200*1.03*1.03 or 200*1.03^2. You'll notice the power is simply the number of years he's been growing. After three years would be 200*1.03^3.
So it ends up being 200* (1.03 to the power of 25)
Good luck with any other questions.
- The “Rule of 72” suggests that an amount will double in 12 years at a 6 percent compound annual rate or double in 6 years at a 12 percent annual rate. Is this a useful rule, and is it an accurate one?
- Have you always wanted to be able to do compound interest problems in your head? Probably not, but it's a very useful skill to have because it gives you a lightning fast benchmark to determine how good (or not so good) a potential investment is likely to be.
The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years.
Yes, it is a useful tool and is reasonably accurate.