SOLUTION: At what rate do you need to invest money into a bank account earning continuously compounded interest if you want to double your money in 62 months?

Question 1140029: At what rate do you need to invest money into a bank account earning continuously compounded interest if you want to double your money in 62 months?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
continuous compounding formula is f = p * e ^ (r * t)

if you want to double your money, then left f = 2 and p = 1.

formula becomes 2 = 1 * e ^ (r * t)

this is the same as 2 = e ^ (r * t)

if you want to do it in 62 months, then the formula becomes 2 = e ^ (r * 62).

take the natural log of both sides of this equation to get:

ln(2) = ln(e ^ (r * 62)

since ln(e ^ (r * 62) is equal to r * 62 * ln(e) and since ln(e) is equal to 1, your formula becomes:

ln(2) = r * 62

divide both sides of this formula by 62 to get:

ln(2) / 62 = r

solve for r to get:

r = .0111797932

replace r in the original equation to get:

2 = e ^ (.0111797932 * 62)

this becomes 2 = 2, confirming the solution is correct.

your interest rate is .0111797932 * 12 = .1341575188 per year.

that's approximately 13.42% per year.

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