Question

Mike withdrew $1,180 from a savings account and invested in common stock. At the end of 5 years, Mike sold the stock for $1,387. In the savings account he would have received an interest rate of 4%, compounded quarterly. He would like to compute a comparable interest rate on his common stock investment.

a) Draw a cash flow diagram for the stock investment

.b) What effective annual interest rate did he receive from the stock investment?

c) Based on quarterly compounding, what nominal annual interest rate did he receive on his investment in stock?

Answer 1

Answer :

(a) Cash flow diagram for the stock investment

(b)

Calculation of Effective annual interest rate from the stock investment

Amount Invested at the beginning of first year $1,180

Amount received at the End of Fifth year = $1,387

Number of years = 5

Compounded quarterly

The formula for future value is :

C = Amount Invested at the beginning of first year

n = Number of years

m = Frequency of compounding in a

By putting amounts in above formula :

i = 0.0081142 x 4

i = 0.0324568

Nominal Annual Interest rate = i = 0.0324568

Compounded quarterly

Effective annual interest rate from the stock investment :

= 1.03285 - 1

= 0.03285

So, Effective annual interest rate from the stock investment = 3.285% per annum

(c)

Calculation of nominal Annual Interest rate

Nominal Annual Interest rate Based on quarterly compounding is already calculated in part b Which is 3.246%