CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
A borrower takes a 200,000 loan to be repaid with 20 equal annual payments, the first due one year from today. The interest rate is 6% per year. The annual payment is closest to:
The annual payment is about 17,437. Divide the 200,000 loan by the 20-year, 6% ordinary annuity factor of about 11.47. Ignoring interest gives 10,000, and treating payments as made at the start of each year gives about 16,450, both wrong here.
- A10,000
- B16,450
- C17,437Correct
Explanation
The annuity factor is (1 - 1.06^-20)/0.06 = 11.4699. Payment = 200,000 / 11.4699 = 17,437. The 10,000 option ignores interest (200,000/20). The 16,450 option divides by an extra (1.06), which would apply to payments made at the start of each year.
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