Interest Rate

Study guides: Exam VEE-ECON, Exam FM-2, Exam 9, Exam INV-201

The interest rate (or rate of interest) i is the amount of interest earned per unit of principal per unit of time. Under Compound Interest, 1 invested grows to (1+i)^n after n periods.

• The interest rate connects Present Value and Future Value:

\text{FV} = \text{PV} \cdot (1+i)^n

\text{PV} = \frac{\text{FV}}{(1+i)^n}

• The effective annual interest rate is the interest earned over a year per unit invested at the start of the year, however often interest is credited during the year — an account credited quarterly whose balance grows 4.5% a year has an effective annual rate of 4.5%. SOA denotes it i, and a nominal rate convertible m times a year i^{(m)}.
• Related measures include the nominal rate convertible m-thly, the Discount Rate, and the Force of Interest.

Finding the Interest Rate An investment of 5{,}000 grows to 6{,}802.44 in 5 years under compound interest. Find the annual effective interest rate.

Answer 6802.44 = 5000(1+i)^5 \implies (1+i)^5 = 1.36049 \implies i = 1.36049^{1/5} - 1 = 0.0635 = 6.35\%