Question

In: Finance

Bob deposits $1,500 at the beginning of each quarter for sixteen years in a fund earning...

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.

Solutions

Expert Solution

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%


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