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March 14th, 2016, 11:16 AM   #1
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Discounted Mean Term

Given this question:

A pension fund will pay out €1 million in arrears for each of the next twenty years from now. The fund contains exactly sufficient money now to cover these liabilities on the basis of an effective interest rate of 7% per annum. This is also the interest rate on which current market prices are calculated and the interest rate earned on cash. The fund wishes to hold 20% of its money in cash and to immediately invest €2 million in a perpetuity bearing interest of 8% per annum payable half-yearly.
It then wants to immediately invest the balance in a zero-coupon bond redeemable at par in n years’ time.

Find:

a) The present value and discounted mean term of the liabilities.

b) The real number n that would make the discounted mean terms of the assets and liabilities equal.
Hint: The discounted mean term of the cash is 0.

Having completed (a), I found the Present Value to be €10,594,000 and the Discounted Mean Term to be 8.316 years.
How do I go about part (b)?

Thanks in advance for any help.
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