Under continuous compounding, the amount of time t in years required for an investment to double is a function of the annual interest rate r according to the formula: t = ln 2 r Use the formula for Exercises 61–63. (See Example 8.) a. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 5.5%? Round to one decimal place. b. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 8%? Round to one decimal place. c. Using the doubling time found in part (b), how long would it take a $3000 investment to reach $12,000 if the interest rate is 8%?
Under continuous compounding, the amount of time t in years required for an investment to double is a function of the annual interest rate r according to the formula: t = ln 2 r Use the formula for Exercises 61–63. (See Example 8.) a. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 5.5%? Round to one decimal place. b. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 8%? Round to one decimal place. c. Using the doubling time found in part (b), how long would it take a $3000 investment to reach $12,000 if the interest rate is 8%?
Solution Summary: The author calculates the time required by the investment to reach 6,000 if the interest rate is 5.5%.
Under continuous compounding, the amount of time t in years required for an investment to double is a function of the annual interest rate r according to the formula:
t
=
ln
2
r
Use the formula for Exercises 61–63. (See Example 8.)
a. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 5.5%? Round to one decimal place.
b. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 8%? Round to one decimal place.
c. Using the doubling time found in part (b), how long would it take a $3000 investment to reach $12,000 if the interest rate is 8%?
The tuition in the school year 2012–2013 at a certain university was $15,000. For the school year 2017–2018, the tuition was $17,850. Find an exponential growth function for tuition T (in dollars) at this university t years after the 2012–2013 school year. (Round your values to four decimal places.)
T =
Assuming it increases at the same annual rate, use the function to predict the tuition (in dollars) in the 2021–2022 school year. (Round your answer to the nearest integer.)
$
Compound Interest In Exercises 53–56, completethe table by finding the balance A when $12,000 isinvested at rate r for t years, compounded continuously.
You invest $800 at 4% interest compounded annually. How much is in the account after 4 years, assuming that you make no subsequent withdrawal or deposit? (Round your answer to two decimal
places.)
$|
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