Finance School of management Example: Reinvesting at a Different Rate You have $10.000 to invest With the two-year CD for two years FT=$10,000×(1.07) Two years CDs and one =$1l449 year CDs are paying 7 and 6% per year With the sequence of respectively two one-year Cds What should you do? Reinvestment rate? FT=$10000×1.07×1.08 You are sure the interest $11448 rate on one-year CDs will be 8% next year uesTc
11 Finance School of Management Example: Reinvesting at a Different Rate ❖ You have $10,000 to invest for two years. ❖ Two years CDs and one year CDs are paying 7% and 6% per year respectively. ❖ What should you do? ❖ Reinvestment rate? ❖ You are sure the interest rate on one-year CDs will be 8% next year. ❖ With the two-year CD $11,449 $10,000 (1.07) 2 = FV = ❖ With the sequence of two one-year CDs $11,448 $10,000 1.07 1.08 = FV =
Finance School of management Frequency of Compounding Annual percentage rate(APR) Effective annual rate (EFF) Suppose you invest $I in a CD, earning interest at a stated APR of 6% per year compounded monthly F=$1×(1+006/12)12=106168 General formul EFF1, APR)m uesTc 12
12 Finance School of Management Frequency of Compounding – Annual percentage rate (APR) – Effective annual rate (EFF) ❖ Suppose you invest $1 in a CD, earning interest at a stated APR of 6% per year compounded monthly. $1 (1 0.06/12) 1.06168 12 FV = + = ❖ General formula 1 −1 = + m m APR EFF
Finance School of management Effective Annual Rates of an APr of 18% Annual Percentage Frequency of Annual effective rate Compounding Rate 18 18.00 2 18.81 18 1925 18 19.56 18 19.68 18 365 19.72 uesTc 13
13 Finance School of Management Effective Annual Rates of an APR of 18% Annual Percentage rate Frequency of Compounding Annual Effective Rate 18 1 18.00 18 2 18.81 18 4 19.25 18 12 19.56 18 52 19.68 18 365 19.72
Finance School of management The Frequency of Compounding Note that as the frequency of compounding increases. so does the annual effective rate What occurs as the frequency of compounding rises to infinity APR EFF=Lim 1+ APr m→ uesTc 14
14 Finance School of Management The Frequency of Compounding 1 = −1 = + → APR m m e m APR EFF Lim ❖ Note that as the frequency of compounding increases, so does the annual effective rate. ❖ What occurs as the frequency of compounding rises to infinity?