Question

Determine the present value of $5000 to be paid in 8 years time if current interest of 10 percent is compounded (a) annually, (b) semiannually, (c) quarterly, and (d) continuously.”

Answer 1

a.

P = F / (1+i)^t

P = 5000 / (1 + 0.1)^8 = 2332.54

= 5000 / (1.1)^8 = 2332.54

b.

i = 0.1 / 2 = 0.05 per semi annual period

Effective interest rate = (1 + 0.05)^2 - 1

= (1.05)^2 - 1

= 0.1025

P = 5000 / (1 + 0.1025)^8

= 5000 / (1.1025)^8 = 2290.56

c.

i = 0.1 / 4 = 0.025 per semi annual period

Effective interest rate = (1 + 0.025)^4 - 1

= (1.025)^4 - 1

= 0.103813

P = 5000 / (1 + 0.103813)^8

= 5000 / (1.103813)^8 = 2268.85

d.

Effective interest rate = e^0.1 - 1

= 1.105170918 - 1

= 0.105170

P = 5000 / (1 + 0.105170)^8

= 5000 / (1.105170)^8 = 2246.66