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Question 1054967: An investment pays simple interest, and quadruples in 13 years. What is the interest rate?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for simple interest is i * p * n.
i is the interest rate per time period.
p is the principal.
n is the number of time periods.
the formula for future value of an investment using simple interest is f = p + p * i * n).
this can be simplified to f = p * (1 + i * n).
you are given that n = 13 years.
you will be looking for the interest rate per year.
since you will be quadrupling your money, than f will be equal to 4p.
your formula of f = p * (1 + i * n) becomes:
4p = p * (1 + 13 * i)
divide both sides of this equation by p to get:
4 = 1 + 13 * i
subtract 1 from both sides of this equation to get:
3 = 13 * i
divide both sides of this equation by 13 to get:
3/13 = i
that's your interest rate per year.
i = 3/13 = .2307692308
for example:
assume your principal is equal to 500 dollars.
your interest in 13 years will be equal to 500 * 3/13 * 13 which will become 500 * 3 which will become 1500 dollars.
add that to your principal of 500 dollars and you get a total of 2000 dollars which is equal to 4 times the original investment of 500 dollars.
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