Part 2. Semi-Annual Compounding Problem 2: What if the bank compounds interest semi-annually? How much is your $100 worth at the end of the year? Amount you invest today (PV) Interest rate bank offers you (r) Compounding period (t) 100.00 6% (0.06 2 Finance Concept: FV = PV * [1+r/t] Future value of $100 invested for one year at 6% semiannually. FV = $100 * (1+.06/2)^2 = $100 * 1.0609 = $106.09 When payments occur more frequently than once a year, or interest is compounded more than once per year, you must: 1) convert the stated interest rate to a periodic rate = Stated rate / Number of payments per year 2) convert the number of years to the number of periods = Number of years * periods per year Note: You are making the rates agree with the periods ! In Words: If we invest one hundred dollars today and the interest rate is six percent and it is compounded twice per year (semi-annually), we will have $106.09. The 1 in the formula represents the principal carried forward for a year. The process of going from today's values to future values is compounding. Hint: remember to always use the equal sign first and don't forget parenthesis! One way to solve this problem in Excel: Enter: =100*(1+.06/2)^2 and hit enter key Try it in cell F94 ==> In Words: If we invest one hundred dollars today and the interest rate is six percent and it is compounded twice per year (semi-annually), we will have $106.09. The 1 in the formula represents the principal carried forward for a year. The process of going from today's values to future values is compounding. Hint: remember to always use the equal sign first and don't forget parenthesis! One way to solve this problem in Excel: Enter: =100*(1+.06/2)^2 and hit enter key Try it in cell F94 ==> Test your skills with this problem: Compute the future value of $300 at 2% paid semi-annually for two years. FV = PV *[1+ r/t]^t PV= 300 =300*(1+0.02/2)^4 0.02 Try it in cell F100 => 4 FV ? Your answer should be => 312.18 r= n = =