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Questions and Answers
What is the formula to calculate the present value of a perpetuity?
What is the formula to calculate the present value of a perpetuity?
What is the main characteristic of a perpetuity?
What is the main characteristic of a perpetuity?
What is the purpose of a loan amortization schedule?
What is the purpose of a loan amortization schedule?
What type of loan has an interest rate that remains the same throughout the loan period?
What type of loan has an interest rate that remains the same throughout the loan period?
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What is the formula to calculate the monthly payment (M) for a loan?
What is the formula to calculate the monthly payment (M) for a loan?
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What is the main difference between a fixed-rate loan and a variable-rate loan?
What is the main difference between a fixed-rate loan and a variable-rate loan?
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If a perpetuity pays $500 per year and the discount rate is 4%, what is the present value?
If a perpetuity pays $500 per year and the discount rate is 4%, what is the present value?
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Study Notes
Time Value of Money: Perpetuity and Loan Amortization
Perpetuity
- A perpetuity is a type of annuity that pays a fixed amount of money at regular intervals indefinitely.
- Formula to calculate the present value of a perpetuity:
- PV = PMT / r
- PV = present value
- PMT = periodic payment
- r = discount rate
- PV = PMT / r
- Example: If a perpetuity pays $100 per year and the discount rate is 5%, the present value would be $100 / 0.05 = $2,000.
- Perpetuities are often used to model dividend payments from a company or interest payments from a bond.
Loan Amortization
- Loan amortization is the process of gradually reducing the principal amount of a loan through regular payments.
- Types of loan amortization:
- Fixed-rate loan: The interest rate remains the same throughout the loan period.
- Variable-rate loan: The interest rate can change over time.
- Formula to calculate the monthly payment (M) for a loan:
- M = (PV x r) / (1 - (1 + r)^(-n))
- PV = present value (initial loan amount)
- r = monthly interest rate
- n = number of payments
- M = (PV x r) / (1 - (1 + r)^(-n))
- Example: If a $10,000 loan has a 6% annual interest rate and a 5-year repayment period, the monthly payment would be approximately $193.33.
- Loan amortization schedules can be used to visualize the payment process and show how much of each payment goes towards interest and principal.
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Description
Understand the concept of perpetuity and loan amortization, including formulas and examples. Learn how to calculate present value, monthly payments, and interest rates.
