Question

4) Determine the value at the end of four years of

a $5,000 investment today that pays a nominal annual interest rate of 15%, compounded:

a)

Annually

b)

Semiannually

c)

Quarterly

d)

Monthly

5. You are considering buying a painting by a local
artist for $1,200. You believe that this artist is just
about to be discovered, and think that five years from now the painting will be worth $5,000. If you are
correct, what average annual return would you earn on this investment over this period?

Answer 1

4. P = 5000

t = 4 years

F = P *(1+i)^t

a) i = 15% compounded annually

F = 5000 * 1.15^4 = 8745.03

b) i = 15% compounded semi annually = 15% / 2 = 7.5% per semiannual period = 0.075

t = 4 years = 8 semi annual periods

F = 5000*1.075^8 = 8917.39

c) i = 15% compounded quarterly = 15% / 4 = 3.75% per quarter = 0.0375

t = 4 years = 4*4 = 16 quarters

F = 5000*1.0375^16 = 9011.14

d) i = 15% compounded monthly = 15% / 12 = 1.25% per month = 0.0125

t = 4 years = 4*12 = 48 months

F = 5000*1.0125^48 = 9076.77

5.

P = 1200, F = 5000, t = 5 year

Let rate of return be i%

Then

5000 = 1200* (1+i)^5

i = (5000/1200)^(1/5) - 1

i = 1.330325 - 1 = 0.330325

i = 33.0325%