1) Short Term Interest Formula

Interest = Principal x rate of return x Time (over 365 days)

Example 1: Best Company borrowed $10,000 based on a short term note payable. Note has an 8% annual interest attached to it and is due in 30 days. Calculate the interest payments?

Solution 1: Interest = 10,000 x 0.08 x 30/365 = $65.75

Example 2: A company borrowed $10,000 due in 90 days. The total interest paid out was $241.15. What was the annual rate of interest?

Solution 2:
241.15 = 10,000 x R x 90/365
241.15 = R x 2465.75
R = 241.15 / 2465.75
R = 0.0978 -> 9.781%

2) Short Term Future Value Formula

Future Value = PV x (1+ R x t)

Example 3: Best Company invested $10,000 into a short-term investment. The investment has an 8% annual interest attached to it and will be paid back in 30 days. What is the future value of this $10,000?

Solution 3: Future Value = $10,000 x (1 + (0.08 x 30/365))
Future Value = $10,000 x (1+ 0.00657)
Future Value = $10,000 x 1.00657
Future Value = $10,065.7

3) Short Term Present Value Formula

Present Value = Future Value / [1+(R x t)] (notice that the present value formula is the same as the Future Value formula, only the FV and PV variables are transposed using algebraic manipulation).

Example 4: Best Company earned $12,500 after investing in a short-term money market instrument for 30 days. The rate of interest earned was 4.5% annual. What original amount was invested in order to earn this $12,500?

Solution 4:
Present Value = 12500 / [ 1+ (0.045 x 30/365)]
Present Value = 12500 / (1 + 0.003698)
Present Value = 12500 / 1.003698
Present Value = $12,453.95

4) Nominal & Effective Interest Rates

A nominal interest rate is a rate that does not have the compounding interest effect included in it. On the other hand, an effective interest rate has the compounding effect built into it. Effective interest rates are the industry standard, used by car dealerships when giving out car loans, banks when giving out business loans, etc.

So how do you convert between a nominal to effective interest rate? The formula is:

Effective Rate = (1 + (i / n))ⁿ - 1
where:
i = Nominal Interest Rate
n = # of compounding periods per year

Example 5: The nominal rate or "stated rate" is 6% compounded semi-annually. What is the Effective Rate?

Solution 5:
Effective Rate = (1 + (0.06 / 2))² - 1
Effective Rate = (1 + 0.03)² - 1
Effective Rate = 1.0609 - 1
Effective Rate = 0.0609 or 6.09%