Question

please answer in terms of j and k and define what each variable stands for

(b) A mutual fund advertises that average annual compound rate of returns for various periods ending December 31, 2015 are as follows: 10 years: 13% , 5 years: 17 %, 2 years: 15%, 1 year: 22%. Find the 5-year average annual compound rates of return for the period January 1, 2006 to December 31, 2010, and find the annual rate of return for calendar year 2014.

Answer 1

Following information provided -

10 years compounding annual rate of return p.a (R) = 13%

which means, Annual return between January 1, 2006 to December 31,2015 is 13%

5 years compounding annual rate of return p.a (r2) = 17%

which means , Annual return between January 1,2010 to December 31, 2015 is 17%

We need to find the Annual compound rate of return between  January 1, 2006 to December 31,2010

Lets Assume, Annual compound rate of return between  January 1, 2006 to December 31,2010 = r1

We can calculate the value of r1 with following equation -

$\dpi{100} (1+r1)^5*(1+r2)^5 = (1+R)^{10}$

$\dpi{100} (1+r1)^5*(1+0.17)^5 = (1+0.13)^{10}$

$\dpi{100} (1+r1)^5 = \frac{(1+0.13)^{10}}{(1+0.17)^5}$

$\dpi{100} (1+r1)^5 = \frac{3.3945673899222}{2.1924480357}$

$\dpi{100} (1+r1)^5 = 1.5483$

$\dpi{100} (1+r1) = 1.5483^{\frac{1}{5}}$

$\dpi{100} (1+r1) = 1.0913675$

$\dpi{100} r1 = 1.0913675-1$

$\dpi{100} r1 = 0.0913675$

$\dpi{100} \bg_green \large r1 = 9.14\%$

Thus, Compounding Annual rate of return between  January 1, 2006 to December 31,2010 is 9.14%

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.