Suppose the force of interest varies over time, according to the function $\delta_t = 0.02t^2$ Kate invests $500 at time 0. At time n, her investment has grown to $2,000 Which of the following is closest to n? Select one: a. 6.4 b. 5.9 c. 5.4 d. 4.9
Added by Juan W.
Close
Step 1
We can set up the equation: 2000 = 500 * e^(integral from 0 to n of 0.02t^2 dt) To solve this equation, we need to find the integral of 0.02t^2 with respect to t. The integral of t^2 is (1/3)t^3, so the integral of 0.02t^2 is (0.02/3)t^3. Now we can rewrite the Show more…
Show all steps
Your feedback will help us improve your experience
Aya Bianca Into and 72 other Principles of Accounting educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Recommended Videos
An investment grows exponentially under continuous compounding. After 2 yr, the amount in the account is \$7328.70. After 5 yr, the amount in the account is \$8774.10. Use the model $A(t)=P e^{r t}$ to a. Find the interest rate $r$. Round to the nearest percent. b. Find the original principal $P$. Round to the nearest dollar. c. Determine the amount of time required for the account to reach a value of $\$ 15,000 .$ Round to the nearest year.
Systems of Equations and Inequalities
Systems of Nonlinear Equations in Two Variables
Suppose that $P_{0}$ is invested in a savings account for which interest is compounded continuously at $4.3 \%$ per year. That is, the balance $P$ grows at the rate given by $\frac{d P}{d t}=0.043 P$ a) Find the function that satisfies the equation. Write it in terms of $P_{0}$ and 0.043 b) Suppose that $\$ 20,000$ is invested. What is the balance after 1 yr? After 2 yr? c) When will an investment of $\$ 20,000$ double itself?
Exponential and Logarithmic Functions
Applications: Uninhibited and limited Growth Models
1 When the interest on an investment is compounded continuously, the investment grows at a rate that is proportional to the amount in the account, so that if the amount present is P then dP/dt = rP, where P is in dollars, t is in years, and r is a constant. If $20,000 is invested (when t = 0) and the amount in the account after 22 years is $280,264, find the function that gives the value of the investment as a function of t. What is the interest rate on this investment?
Carolyn B.
Recommended Textbooks
Horngren’s Cost Accounting
Cost Accounting A Managerial Emphasis
Principles of Accounting Volume 1: Financial Accounting
Watch the video solution with this free unlock.
EMAIL
PASSWORD