SOLUTION: Find the total value An when a principle P is invested at 12% p.a. simple interest for n years. Hence find the smallest number of years required for the investment to double.

Question 1125107: Find the total value An when a principle P is invested at 12% p.a. simple interest for n years. Hence find the smallest number of years required for the investment to double.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for simple interest is i = n * p * r

i is the interest
n is the number of time periods
p is the principal
r is the interest rate per time period.

when the investment is doubled, the interest is equal to the principal.

the formula becomes p = n * p * r

divide both sides of this equation by po to get 1 = n * r

divide both sides of this equation by r to get 1 / r = n

since r = .12, the formula becomes 1 / .12 = n which results in n = 8 and 1/3 years.

that's how long it will take for the money to double.

the total future value of the investment is given by the formula f = p + i.

when i = p, the formula becomes f = p + p which results in f = 2 * p, meaning the money has doubled.

so the minimum number of years for the money to double would be 8 and 1/3 years.

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