Question

a) What’s the future value of $100 after 3 years if it earns 8%, annual compounding?

b) What’s the present value of $100 to be received in 3 years if the interest rate is 8%, annual compounding?

c) What annual interest rate would cause $1,000 to grow to $2,000 in 8 years?

d) If a company’s sales are growing at a rate of 7.2% annually, how long will it take sales to double?.

e) What is the present value of a 6-year, $100 ordinary annuity if the annual interest rate is 4%?

Answer 1

A. Present Value (PV) = $ 100 Time Period (N) = 3 Years Interest (R) = 8 % Future Value = PV *(1+R%)^N Future Value = 100 *(1+8%)^3 Future Value = 100 * (1.08)^3 Future Value = 100 * 1.2597 Future Value = 1,25.98 PV = ? Future Value = $ 100 N = 3 years R = 8% Present Value (PV) = FV/(1+R%)^N Present Value (PV) = 100/(1+8%)^3 Present Value (PV) = 100/(1.08)^3 Present Value (PV) = 100 / 1.2597 Present Value (PV) = 79.38 Future value is $ 125.98 Present Value = $ 79.38

Annual Interest Rate R = ? Present Value (PV) = $1,000 Future Value (FV) = $2,000 Time Period (N) = 8 Years Sales to be double in how many years, N = ? Lets assume Present Sales = 5 Lets assume Future Sales = 25 Growth rate = G = 7.2% Annual Future Value = PV *(1+R%)^N Future Sales - Present Sales *(1+R%) ^N R= ((FV/PV)^1/N)-1 Future Sales /Present Sales = (1+7.20%)^N R= ((2000/1000)^(1/8))-1 2 = 1.0720 ^N R = (2^0.125) -1 Solving by Hit and Trial method, For N =10 years, 1.0720 * 10 =2 R = 1.090508 -1 = 0.090508 = 9.051% Hence, Sales get double in 10 Years. Hence, Interest Rate = 9.051%

E. To find present value of ordinary annuity Annual interest rate R=4% Time period = 6 Years Annity (Cash flow ) = $ 100 Present value of annuity is sum of product of annuity and discount factors. Present value of annuity = Annuity * ( D1 + D2 + D3 + D4 + D5 +D6 ) Discount Factos: D1 = 1/(1+R%)^1 = 0.961538 D2 = 1/(1+R%)^2 = 0.924556 D3 = 1/(1+R%)^3 = 0.888996 D4 = 1/(1+R%)^4 = D5 = 1/(1+R%)^5 D6 = 1/(1+R%)^6 = 0.790315 0.854804 0.821927 Sum of discount Factor = 5.2421 PV of annuity = 100 * 5.242137 = 524.21 PV of annuity is $ 524.21