Find the value of an amount invested for different compounding periods, Problem 1: You invest S100 in your bank for one year. You camn 6% per annum. What is your $100 worth at the end of the year? Part 1. Annual Compounding 100.00 Amount you invest today(PV) Interest rate bank offers you (r) Compounds periods 6% (0.06) 1 (annual) PV - Present Value or beginning amount - number of compounding periods FV-Future Value or ending amount -interest rate (per year) Finance Concept: Future Value of a Lump Sum-Principal (1+r) FV-PV (1+r) FV-S100 (1+.06) - S1001.06 - $106 In Words: If we invest one hundred dollars today and the interest rate is six percent and it is compounded once per year (annually), we will have $106 at the end of the year (Future Value). The compounded amount is equal to the beginning amount plus the interest earned. You are lending the bank your money and they are paying you for that privilege To answer the problem fill in the indicated cells. One way to do this using Excel: In cell H31 Enter: -100*1.06 and hit enter key cell 31- Hint: Remember to always use the equal sign first! Another way using cell formulas: Enter 100 in cell G37> Enter 1.06 in cell G38 To calculate: In cell G39 type the following formula: G37*G38 and hit the enter key You can write the formula directly, or you can use your mouse to click on the cells. Test your skills with this problem: Compute the future value of $300 at 2% for one year Your answer should be PV- $306 1.02 FV- Finance Concept: We can generalise and get the following formule (where - time: FV-PV (1+r) Note: 'n' is also used for "number of periods, and with calculator The (ltr)'t part of the formula tells us that we are caring compound interst. or interest on interest at the rate, r, fort periods In Words: If we invest one hundred dollars today (PV-S100) and the interest rate is six percent and it is compounded once per year (annually), after five years (1-5), the Future Value FV2 - 100 (1.0615 will be 100(1.338226) - $133.822. We write the formula in Excel as: - 100"(1.06) 5. We camed S30 from 6% simple interest (5 yrs @.06 = $30) plus an extra $3.82 from compounding, Hende the "Magic of Compounding