QQuestionMathematics
QuestionMathematics
Calculate the present value of a $\$ 10,1$ perpetuity at a 6 percent discount rate.
Calculate the future value of an annuity of $\$ 5,1$ each year for eight years, deposited at 6 percent.
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:I'll solve both problems step by step using precise LaTeX formatting:
Problem 1: Present Value of Perpetuity
Step 2:: Recall the perpetuity present value formula
- $$r$$ = Discount rate
Where:
Step 3:: Plug in the given values
- $$C = \$10,000
- r = 0.06 (6%)
Step 4:: Calculate the present value
PV = \frac{\$10,000}{0.06} = \$166,666.67
Final Answer
Problem 2: Future Value of Annuity Step 1: Use the future value of annuity formula FV = PMT \cdot \frac{(1 +r)^{n}- 1}{r} Where: - PMT = Periodic payment - r = Interest rate - n = Number of periods Step 2: Plug in the given values - PMT = \$5,000 - r = 0.06 (6%) - n = 8 years Step 3: Calculate the future value FV = 5,000 \cdot \frac{(1 + 0.06)^{8}- 1}{0.06} FV = 5,000 \cdot \frac{1.5938 - 1}{0.06} FV = 5,000 \cdot \frac{0.5938}{0.06} FV = 5,000 \cdot 9.8967 FV = \$49,483.50
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students