M.Y. Mutual Fund provides a retirement fund that has a liability to pay out RM 100,000 at the end of one year, followed by RM 105,000 at the end of two years and the amount keeps increasing till the end of RM 20 years with RM 195,000 as the last payment. The fund values these payments using an effective rate of interest 7%. The interest rate to calculate the current prices of all bonds are also 7%. In order to be able to pay out the amount stated above, the fund invests an amount equal to the present value of these liabilities in the following two assets:

i) A zero-coupon bond redeemable in 25 years, and

ii) A fixed interest bond redeemable at par in 12 years time with a coupon rate of 8% per annum

a) Calculate the present value and the duration of the liabilities

b) Calculate the amount of cash that should be invested in each of the assets if the duration of the assets is equal to the liabilities