Question

a. Calculate the future value of a $1 investment paying interest of 13.7% compounded annually. Work out the value of the investment after 1, 5, and 20 years.

b. Calculate the future value of a $1 investment paying interest of 13.5% compounded semiannually. Work out the value of the investment after 1, 5, and 20 years.

c. Calculate the future value of a $1 investment paying 13.3% compounded continuously. Work out the value of the investment after 1, 5, and 20 years.

d. Which investment would you prefer?

Answer 1

Future value (FV) = Present Value(PV)*(1+r)ⁿ

a) PV =$1, r = 13.7%

n= 1 FV = 1*(1+0.137)¹ = 1.137

n= 5 FV = 1*(1+0.137)⁵ = 1.9002

n= 20 FV = 1*(1+0.137)²⁰ = 13.0379

b) PV =$1, i = 13.5%, r = 0.135/2 = 0.0675

n= 1*2=2 FV = 1*(1+0.0675)² = 1.1396

n= 5*2=10   FV = 1*(1+0.0675)¹⁰ = 1.9217

n= 20*2=40 FV = 1*(1+0.0675)​⁴⁰​​​​​​ = 13.6369

c) compounded continuously P(t) =P₀e^rt

P₀= 1, r = 13.3% (0.133), e = 2.7183

t=1 FV = 1*e^(0.133*1) = 1*2.7183^(0.133*1) = 1.1423

t=5 FV = 1*e^(0.133*5) = 1*2.7183^(0.133*5) =1.9445

t=20 FV = 1*e^(0.133*20) = 1*2.7183^(0.133*20) =14.2965

d) c Investment I prefer (compounded continuously)

even the rate of interest is low compared to a&b the FV is high among a&b because of compounded continuously. so i prefer Investment in (c)