In: Finance
Bob deposits $1,500 at the beginning of each quarter for sixteen years in a fund earning a nominal rate of interest of 6% convertible monthly. The interest from this fund is paid out monthly and can only be reinvested at an effective annual rate of 5.2%. Find Bob’s yield rate for the twenty-year period.
For the first 16 years :
The effective rate of interest ( R ) for an account paying a nominal rate ( r) , compounded (k) times per year, is where is the periodic rate, .
R = ( 1+ i )^ k – 1 i = r/k
=(1 + 0.06/12)^12-1
=(1+0.005)^12 – 1
=6.168%
For the next 4 years :
=5.2%
Thus for total 20 years = [ ( 6.168 x 16) + ( 5.2 x 4 ) / 20 ]
= 5.97%