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

Question #233745
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?
1
Expert's answer
2021-09-15T02:13:37-0400




• 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\\%"


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