Answer to Question #233745 in Civil and Environmental Engineering for Alan Enrico V Tuib

Question

Mr. Sansome withdrew $1000 from a savings account and invested it in common stock. At the end of 5 years, he sold the stock and received a check for $1307. If Mr. Sansome had left his $1000 in the savings account, he would have received an interest rate of 5%, compounded quarterly. Mr. Sansome would like to compute a comparable interest rate on his common stock investment. Based on quarterly compounding, what nominal annual interest rate did Mr. Sansome receive on his investment in stock?

Answer 1

• Investment was made a year ago and return was obtained a year from now so it means 2 successive years

.i.e. T=2 years

• Assuming it to be compounded annually from 90$To 110$

$A=P(1+\frac{R}{100} \times n )^{nT}$ ,where n=no of times it is compounded annually, t= no of years

$110=90(1+\frac{R}{100})2$ , because $n=1$ $(\frac{110}{90})(1/2)=1+\frac{R}{100}$

$R=((\frac{110}{90})1/2-1)\times100=10.55\%$

• Assuming it to be simple interest

$I=P\times R \times T$

$20=\frac{(90\times R \times2)}{100}$

$R=\frac{(20\times100)}{2\times90}=11.11\%$