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)


R
=
(
20
×
100
)
2
×
90
=
11.11
%
R=
2×90
(20×100)

=11.11%