Multiple Choice
If John takes out a \$10,000 loan at an annual interest rate of 6\% compounded annually for 5 years and repays the loan in equal annual installments, how much total interest will he pay over the course of the loan?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
Which one of the following is an ordinary annuity, but not a perpetuity?
A
A single lump-sum payment made after 5 years
B
A series of equal payments made at the end of each year forever
C
A series of equal payments made at the beginning of each year forever
D
A series of equal payments made at the end of each year for 10 years
Verified step by step guidance1
Step 1: Understand the definitions of key terms. An ordinary annuity is a series of equal payments made at regular intervals, typically at the end of each period, for a specified number of periods. A perpetuity, on the other hand, is a series of equal payments made at regular intervals that continue indefinitely.
Step 2: Analyze the options provided in the problem. The first option describes a single lump-sum payment, which does not qualify as an annuity or perpetuity. The second and third options describe payments that continue forever, which are characteristics of a perpetuity.
Step 3: Focus on the fourth option: 'A series of equal payments made at the end of each year for 10 years.' This matches the definition of an ordinary annuity because the payments are equal, occur at regular intervals (end of each year), and are limited to a specific time frame (10 years).
Step 4: Compare the characteristics of the fourth option to the definitions of an ordinary annuity and a perpetuity. Since the payments do not continue indefinitely, it cannot be a perpetuity. However, it fits the criteria for an ordinary annuity.
Step 5: Conclude that the correct answer is the fourth option, as it represents an ordinary annuity with a finite duration of 10 years.
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