|
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.
|
|
|
| |
