SOLUTION: 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

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.

RELATED QUESTIONS
you have $75 and invest it into an account that gives 2.5% annual interest and compounds... (answered by stanbon,MathTherapy)

You decided to invest $500 into a savings account that compounds at a rate of 2.5%... (answered by ikleyn)

10 years ago you placed $4000 into an account at Chase Bank. The account compounds... (answered by math_tutor2020,josgarithmetic)

Suppose that when you were born, your grandparents deposited $1000 into an account that... (answered by Fombitz)

Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How... (answered by math_helper)

Suppose that you invest $100 at an annual interest rate of 4.8% compounded continuously.... (answered by Alan3354,MathLover1)

Suppose you invest $500 at an annual interest rate of 7.1% compounded continuously. How... (answered by ikleyn)

another question for y'all suppose you invest $5000 into an interest-bearing account... (answered by jim_thompson5910)

Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How... (answered by rfer)