Question

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%. This is just as in Problem (4.5.5). Find Bob’s yield rate for the twenty-year period.

Answer 1

Answer:

Net Yield = 6.27%

Explanation:

This question can be broken down into 2 parts:-

1) First 16 years return, which is more complex one

2) Next 4 years, which is simpler one

1) First 16 years return:-

Interest Paid on the initial fund is 6%. Total Interest earned can be easily calculated:-

(64+63+62+....+1)*1500*0.015=46,800 use 1+2+3...+n = n(n+1)/2

Now this interest can be further invested i@5.2% anually

1500 for 3 months each month we get 7.5 for 1500 invested so series will be (7.5+7.5+7.5+15+15+15+...480+480+480).

Return will be 5.2%/12(7.5*192+7.5*191+7.5*190+15*189+15*188+15*187+.....+480*3+480*2+480*1), this can further be written as 0.0043*7.5*{1(192+191+190)+2(189+188+187)....+64(3+2+1)), on solving this we will get 13,182

We have total principal of 96000 and total interest of 59,982.

Net yield = 6.15%

2) For next 4 yaers:-

Principal will earn constant return of 6%, i.e., 96000*6%=23,040

This interest + earlier interest will earn 5.2% anually

96000*5.2%/12*(1+2+3+...+48) = 2,446.08

59,982*5.2%*4=12476.25

Total Interest earned =111,126

Net Yield = 6.27%