Question 1192786: Suppose you invest $600 into an account that compounds continuously at a rate of 1.75%. How long would you have to leave the money in the account to have an ending balance of $1350?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! formula for continuous compounding is:
f = p * e ^ (r * n)
f is the future value
p is the present value
r is the rate per time period
n is the number of time periods.
your time periods are in years.
with p = 600 and f = 1350 and r = .0175, the formula becomes:
1350 = 600 * e ^ ( .0175 * n)
note that the decimal equivalent of the rate is used, not the percent.
decimal equivalent of rate = percent / 100.
1.75% = .0175.
divide both sides of 1350 = 600 * e ^ ( .0175 * n) by 600 to get:
2.25 = e ^ (.0175 * n)
take the natural log of both sides of this equation to get:
ln(2.25) = .n(e ^ (.0175 * n)
because ln(e^x) = x*ln(e) and ln(e) = 1, the equation becomes:
ln(2.25) = .0175 * n
divide both sides of this equation by .0175 and solve for n to get:
n = ln(2.25) / .0175 = 46.3388695.
confirm by replacing n in the equation with that to get:
f = 600 * e ^ (.0175 * 46.3388695) = 1350.
this confirms the value of n is good.
your solution is that you would have to leave the money in the account for 46.3388695 years to allow it to grow to 1350 at 1.75% per year compounded continuously.
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