Question

You spent $ 355 and you get $ 860 back at the end of 5 years. Use the interest and interpolation tables by hand to determine the internal rate of return. Displays the interpolation on the spreadsheet.

Answer 1

We know that

Future value= present value*(1+r)^n

Future value = 860$

present value=355$

r= internal rate of return we need to find

n= no of years - 5

1.Assuming r= 15%

= 355*(1+15%)^5=355*(1.15)^5= 714.03 which is less than 860 so r is greater than 15%

2. Assuming r= 25%

= 355*(1+25%)^5=355*(1.25)^5= 1083.374 which is more than 860 so r is less than 25%

3. Assuming r= 20%

= 355*(1+20%)^5=355*(1.20)^5= 883.3536 which is more than 860 so r is less than 20%

By this we can say that r lies between 15% and 20% so

by interpolation r=

at r=	obtained Value (A)	Future value-obtained value
15%	714.03	=860-714.03=145.97
25%	1083.374	=860-1083.374=-223.374
20%	883.3536	=860-883.3536=-23.3536

r=15%+(20%-15%)*(145.97)/(145.97-(-23.3536))

=15%+(5%)*145.97/(169.3236)

=15%+4.31= 19.31%

or at

A	15%	714.03
B	20%	883.3536
(A-B)	-5%	-169.324

=860-714.03= 145.97

so if at 5% the difference in value is   169.324

so for $145.97= 145.97*5%/ 169.324= 4.34%

so r= 15%+4.34%=19.35%(rounded offf)

so IRR internal rate of return -19.3%