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+R100×n)nTA=P(1+\frac{R}{100} \times n )^{nT} ,where n=no of times it is compounded annually, t= no of years

110=90(1+R100)2110=90(1+\frac{R}{100})2 , because n=1n=1 (11090)(1/2)=1+R100(\frac{110}{90})(1/2)=1+\frac{R}{100}

R=((11090)1/21)×100=10.55%R=((\frac{110}{90})1/2-1)\times100=10.55\%

• Assuming it to be simple interest

I=P×R×TI=P\times R \times T

20=(90×R×2)10020=\frac{(90\times R \times2)}{100}

R=(20×100)2×90=11.11%R=\frac{(20\times100)}{2\times90}=11.11\%


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