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 $1000 in the savings account, he would have received an interest rate of 5%, compounded quarterly. Mr. Sansome would like to compute a comparable interest rate on his common stock investment. Based on quarterly compounding, what nominal annual interest rate did Mr. Sansome receive on his investment in stock?
Investment was made a year ago and return was obtained a year from now so it means 2 successive years .i.e. T=2 years • Assuming it to be compounded annually from 90$To 110$ A = P ( 1 + R 100 × n ) n T A=P(1+ 100 R ×n) nT ,where n=no of times it is compounded annually, t= no of years 110 = 90 ( 1 + R 100 ) 2 110=90(1+ 100 R )2 , because n = 1 n=1 ( 110 90 ) ( 1 / 2 ) = 1 + R 100 ( 90 110 )(1/2)=1+ 100 R
R = ( ( 110 90 ) 1 / 2 − 1 ) × 100 = 10.55 % R=(( 90 110 )1/2−1)×100=10.55% • Assuming it to be simple interest I = P × R × T I=P×R×T 20 = ( 90 × R × 2 ) 100 20= 100 (90×R×2)
