A 30-year home mortgage is a classic example of
a. a set of unequal cash flows.
b. an ordinary annuity
c. a perpetuity
d. an annuity due.
e. a consol.
The Correct Answer and Explanation is:
Correct Answer: b. an ordinary annuity
Explanation:
A 30-year home mortgage is a financial product that involves making equal monthly payments over a fixed period of time, typically 30 years, to repay a loan with interest. This structure fits the definition of an ordinary annuity.
What is an Ordinary Annuity?
An ordinary annuity is a sequence of equal payments made at regular intervals, such as monthly or annually, with payments occurring at the end of each period. In the case of a mortgage:
- The borrower makes fixed payments (covering both principal and interest).
- Payments are typically made at the end of each month.
- The term is fixed—30 years, or 360 months.
Each monthly payment is calculated based on the loan amount (principal), the interest rate, and the loan term. Over time, the portion of the payment that goes toward interest decreases, while the portion applied to the principal increases.
Why the Other Options Are Incorrect:
- a. A set of unequal cash flows:
A mortgage involves equal monthly payments, not unequal ones. While the distribution between interest and principal changes, the total payment remains constant, making this incorrect. - c. A perpetuity:
A perpetuity involves payments that go on forever. A 30-year mortgage has a fixed end point, so it is not a perpetuity. - d. An annuity due:
An annuity due involves payments made at the beginning of each period. Mortgages require payments at the end of each month, making this choice incorrect. - e. A consol:
A consol is a type of perpetual bond that pays interest forever without repaying principal. Mortgages are not bonds, and they end after 30 years, so this is also incorrect.
Conclusion:
A 30-year home mortgage is a classic example of an ordinary annuity because it involves equal payments made at the end of each month over a fixed term. This regular, predictable structure is why mortgages are often used to explain the concept of ordinary annuities in finance.