Hi, please need help with this, notes state to Draw Time Lines & Show Calculator Work.

Thank you.

Time Value of Money-Additional Practice Draw Time Lines & Show Calculator Work!! 1. What amount received at the end of 20 years is equivalent to $100 today, given an opportunity cost of 14%? Equivalent Amount = Present Value x (1 + r)^n Equivalent Amount = 100 x (1 + 0.14)^20 = $1,374.35 PV = 100 0 20 1 n = Number of Years = 20 2 3 r = Rate of Interest = 14% 4 9 5 6 7 8 10 11 12 13 FV = 1,374.35 14 15 16 17 18 19 2. What amount received at the end of 15 years is equivalent to $100 received at the end of each year for 15 years, given an opportunity cost of 12%? Formula to calculate future value of annuity = PMT / i [(1 + i)^n - 1] Future Value of $100 received at the end of each year = 100 / 0.12 [(1 + 0.12)^15 - 1] Equivalent amount at the end of 15 Years = $3,728 PMT 0 100 1 100 100 100 100 100 100 100 2 3 4 5 6 7 8 n = Years = 15 100 100 9 10 100 100 100 100 100 11 13 14 15 12 I = Interest = 12% FV = $3,728 3. What present amount is equivalent to $100 received at the end of 5 years, given an opportunity cost of 16%? Formula to calculate Present amount = P = A / (1 + r)t Present Amount = 100 / (1 + 0.16) ^5 Present Amount = $47.61 PV = $47.61 FV = $100 0 1 2 r = Interest =16% 3 4 5 t = Years = 5 4. What present amount is equivalent to $100 received at the end of each year for 8 years, given an opportunity cost of 20%? Formula to calculate Present amount = PMT / i [1 - 1 / (1 + i) ^n] Present amount Equivalent = 100 / 0.20 [1 - 1 / (1 + 0.20) ^8] Present amount Equivalent = $384 0 1 2 PV= $384 100 100 3 4 100 100 n = Years = 8 5. 5 6 100 7 100 100 8 100 I = Interest = 20% Find the future value in 2 years of $100 that is deposited in an account which pays 12% compounded monthly. Formula to calculate Future Value = A = P(1 + r)nt A = 100 (1 + 0.12 / 12)^12x2 = $127 0 1% 1% 1% PV = 100 1% 1% 1% 1% 1% 1% 1% 1% 1% 24 Monthly Compounding 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1%1 % I = 1% per month FV = $127 6. Find the present value of $100 to be received at the end of 2 years if the discount rate is 12% compounded monthly? Formula to Calculate Present Value = P = A / (1 + r)nt P = 100 / (1 + 0.12 / 12)^12x2 = $78.76 0 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% PV = $78.76 24 Monthly Compounding 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1%1 % I = 1% per month FV = $100 7. Find the present value of a perpetuity of $1500 per year given a 20% opportunity cost. Present Value of Perpetuity = Annual Payment / Opportunity Cost Present Value of Perpetuity = 1,500 / 0.20 = $7,500 Year 0 PV = $7,500 1 2 1,500 1,500 Opportunity Cost = 20% 3 4 1,500 1,500 5 1,500 Time = Perpetual 8. If the present value of a perpetuity is $6000 ant the discount rate is 8%, what is the amount of the annuity payments? Annuity Payment = Present Value x Discount Rate Annuity Payment = 6,000 x 8% = $480 Year 0 1 2 PV = $6,000 480 3 4 5 480 480 480 480 Discount Rate = 8% Time = Perpetual 9. At an 8% interest rate, how long does it take for a sum of money to double? Time required to Double the money according to rule of 72 = 72 / Interest Rate Time required to Double the money according to rule of 72 = 72 / 8 = 9 Years 0 PV=100 1 2 3 4 5 6 n = 9 Years 7 8 9 FV = $200 10. What is the rate of return on an investment if you lend $100 and 2 years later are repaid $1254.70? Formula to calculate Rate of return = r = [(A/P)1/t - 1] R = [(1254.70 / 100)^1/2 - 1] = 254.22% Year 0 PV = $100 1 I = Interest = 254.22% t = 2 Years 2 FV = $1,254.70