2 a) A pension fund receives contributions and pays out some benefits accordingly. The fund value is reported every after transaction and at the year end. The details during the year 2019 are as follows:

i) Calculate the dollar-weighted rates of return ii) Calculate the time-weighted rates of return

b) Johny has RM 10,000 and plans to make some investments. The first investment, he wants to purchase an annuity with payments of RM 1,000 at the beginning of each year at an effective annual interest rate of 8%. The returns of the annuity payments are then reinvested at an effective annual interest rate of 7%. The second investment is on the remaining balance from the RM 10,000, that is then invested in a 10-year certificate of deposit with a nominal rate of 9% compounded quarterly. Calculate the annual effective yield rate on the entire 10,000 investment over the 10-year period.

Transactions Fund Values Date 1/1/2019 1/3/2019 1/9/2019 1/11/2019 1/1/2020 Amount 2,000,000 2,480,000 3,200,000 2,160,000 1,800,000 Benefits paid 31/10/2019 31/12/2019 1,000,000 400,000 Contributions Received 29/2/2019 31/8/2019 400,000 400,000 Transactions Fund Values Date 1/1/2019 1/3/2019 1/9/2019 1/11/2019 1/1/2020 Amount 2,000,000 2,480,000 3,200,000 2,160,000 1,800,000 Benefits paid 31/10/2019 31/12/2019 1,000,000 400,000 Contributions Received 29/2/2019 31/8/2019 400,000 400,000