Interest

Study guides: Exam FM-2, Exam FAM

Interest is the compensation paid by a borrower to a lender for the use of money over time. It is the fundamental mechanism of the time value of money.

• The interest paid in period t of a loan is:

I_t = i \cdot B_{t-1}

• where i is the periodic Interest Rate and B_{t-1} is the Outstanding Balance at the start of the period.
• In a level-payment Amortization schedule, the interest portion of each payment decreases over time as the balance is paid down, and the principal repayment portion increases correspondingly:

P_t = \text{Payment} - I_t

= \text{Payment} - i \cdot B_{t-1}

Interest vs. Principal Split A 10{,}000 loan at 5\% annual interest is repaid with 3 equal annual payments. Find the interest and principal in the first payment.

Answer Payment = 10000/a_{\overline{3}|5\%} = 10000/2.7232 = 3672.09. Interest in year 1: I_1 = 0.05 \times 10000 = 500. Principal repayment: P_1 = 3672.09 - 500 = 3172.09.