ch5A - 1 0 ower Point Presentation designed by Dr. Sylvia...

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Unformatted text preview: 1 0 ower Point Presentation designed by Dr. Sylvia C. Hudgins for Finance 323 at ODU Compound Value Parameters: Interest rate (i) [The text uses r in notation] Interest Amount that is invested, present value (PV) Time money remains invested (n) Future value of the investment in n years (FVn) Periodic equal payment (or deposit) (PMT) 2 Compound Value 3 Future Value of a Lump Sum (one time payment): Value at some time in the future of an investment Interest compounds: earn interest on interest in later Interest years. years. Future value in one year is present value plus the Future interest that is earned over the year. interest Compound Value 4 Future Value of a Lump Sum (one time payment): Value at some time in the future of an investment Interest compounds: earn interest on interest in later Interest years. years. Future value in one year is present value plus the Future interest that is earned over the year. interest FV1 = PV + (PV x i) Example: Invest $100 for 1 year at 6%: FV1 = 100 + (100 x 0.06) = $106.00 5 Compound Value Future Value of a Lump Sum (one time payment): Extend to 2 years: FV2 = PV + (PV x i) + (PV x i) + PV x i x i 1st year interest on Principal 2nd year interest on Principal 2nd year interest on interest FV2 = 100 + (100 x.06) + (100 x .06) + (100 x .06 x .06) = 112.36 In General: FVn = PV(1+ i)n Compound Value 6 Future Value of a Sum (one time payment): Example: Deposit $256 at an 8% interest rate, how Example: much can you withdraw in 1 year, 2 years, 16 years? much FV1 = 256+256(0.08) = $276.48 FV2 = 256+256(0.08)+256(0.08)+256(.08).08 = 256+20.48+20.48+1.64 = $298.60 = 256(1+.08)2 = $298.60 FV16 = 256(1+.08)16 = $877.08 7 Compound Value Future Value of a Sum (one time payment): Graphically: Deposit $256 today, what is Future Graphically: Value? Value? $1000 900 i = 8% 800 700 600 500 i = 4% 400 300 200 0 i = 0% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Year Compound vs. Simple Interest 8 Compound interest: Interest earned on both the Compound initial principal and the interest reinvested from prior periods. prior Simple interest : Interest earned only on the Simple original principal amount invested. original Consider the previous example(Deposit $256 at Consider an 8% interest rate, how much can you withdraw in 16 years? in FV with compound interest = 877.08 FV with simple interest = 256 + (16*20.48) = 583.68 The extra 293.40 comes from the interest paid on the interest 9 Discounted Value Present Value of a Lump Sum (one time payment): Value today of an amount to be received or paid in Value the future. the FV n PV = (1 + i)n Example: Expect to receive $100 in one year. If can invest at 10%, what is it worth today? 0 PV = 100 = 90.90 (1+.1) 1 $100 2 10 Discounted Value Present Value of a Lump Sum (one time payment): Value today of an amount to be received or paid in Value the future. the FV8 PV = (1 + i)8 Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 100 = 46.65 PV = (1+.1)8 1 2 3 4 5 6 7 8 $100 11 Discounted Value Present Value of a Sum (one time payment): Graphically: Present Value of $100 to be received in Graphically: the future. the $100 90 i = 0% 80 70 60 i = 5% 50 40 30 20 0 i = 10% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Year Financial Calculator Setting Display Should show 9 decimal places on your Should calculator when you are performing calculations. calculations. Financial calculators contain a number of Financial memory registers. These registers should be cleared of work to prevent carry-over errors. (CLR TVM) (CLR Compounding should be set to once per Compounding period (P/YR=1), not the factory setting of 12. 12. 12 13 Compound Value Future Value of a Sum (one time payment): Example: Deposit $256 at an 8% interest rate, how Example: much can you withdraw in 16 years? much FV16 = 256(1+.08)16 = $877.08 Interest rate (i)= Amount that is invested (PV)= (Remember sign convention) number of periods (n)= Future value (FVn)= Periodic equal payments Periodic (PMT)=0 (PMT)=0 877.08 N 16 I/YR PV PMT FV 8 -256 0 ? 14 Discounted Value Present Value of a Lump Sum (one time payment): Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 100 = 46.65 PV = (1+.1)8 Interest rate (i)= Amount that is invested (PV)= number of periods (n)= Future value (FVn)= Periodic equal payments Periodic (PMT)=0 (PMT)=0 -46.65 N 8 I/YR PV PMT FV 10 ? 0 100 15 Compound/Discounted Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the Given fourth can be computed. fourth Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 Can Solve Using Either: FVn PV = or FVn = PV(1+ i)n (1 + i)n In General: In i= ( FV PV 1 n ) -1 230 = 200(1+ i)2 230 = (1+ i)2 200 1.15 = (1+ i)2 1.0724 = 1+ i i = .0724 = 7.24% 16 Compound/Discounted Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the Given fourth can be computed. fourth Example: How long will it take for a $300 investment to grow to $500 if 6% annual interest is earned? 0 $300 1 N $500 Can Solve Using Either: 500 = 300(1+ .06)N FVn PV = or FVn = PV(1+ i)n 500 = (1+ .06)N (1 + i)n 300 ln(1.667) = N ln(1+ .06) General Formula: N = ln(1.667) ln (FV/PV) ln(1.06) N = ln (1 + i) N = 8.77 years Quick Quiz: 17 What is the difference between simple interest and What compound interest? (How would you calculate each?) What is the relationship between present value and future value? (How would you calculate each?) What are some situations where you might want to compute the implied interest rate? (How would you calculate the interest rate?) (Remember the sign convention on the calculator) sign When might you want to compute the number of When periods? (How would you calculate the number of periods?) of ...
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