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CFA Level I · CFA Level I Exam · The Time Value of Money in Finance

A borrower takes a 100,000 loan at 6% per year, repayable in three equal annual end-of-year payments. The principal repaid within the second payment is closest to:

The principal repaid in the second payment is about 33,296. The level payment is 37,411; after Year 1 the balance is 68,589, so Year 2 interest is about 4,115, and the remainder of the payment reduces principal. Using the Year 1 principal or the full payment is wrong.

  1. A31,411
  2. B33,296Correct
  3. C37,411

Explanation

Payment = 100,000 × 0.06 / (1 − 1.06^−3) = 37,411. Year 1 interest is 6,000, so principal is 31,411 and the balance is 68,589. Year 2 interest is 4,115, so principal repaid is 37,411 − 4,115 = 33,296. The 31,411 figure is the Year 1 principal and 37,411 is the whole payment.

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