Actuarial Notes

Principal

Study guides: Exam FM-2, Exam GI-301

The principal L is the original amount borrowed in a loan.

  • It is the basis on which interest is computed in the first period (\text{Interest}_1 = L \times i).
  • Over the life of an amortized loan, each payment covers interest on the Outstanding Balance plus a portion of principal repayment; the outstanding balance decreases until the entire principal has been returned to the lender by the final payment.
  • The distinction between principal and interest is important for tax purposes, accounting, and the construction of an Amortization Schedule.

Principal vs Interest in a Loan Payment A borrower takes out a $15{,}000 loan at 6\% annual interest, to be repaid with level annual payments over 5 years. How much of the very first payment is principal and how much is interest?

Answer Payment: P = 15000 / a_{\overline{5}|6\%} = 15000 / 4.212364 = \$3{,}560.95

Interest in payment 1: I_1 = L \times i = 15000 \times 0.06 = \$900.00

Principal in payment 1: PR_1 = P - I_1 = 3560.95 - 900.00 = \$2{,}660.95

After the first payment the outstanding balance is 15000 - 2660.95 = \$12{,}339.05. In subsequent payments the interest portion shrinks and the principal portion grows, but the total payment stays constant at $3{,}560.95.