solve without excel (c), A 30-year 20,000 bond that pays 3% annual coupons matur

Question

solve without excel (c), A 30-year 20,000 bond that pays 3% annual coupons matures at par. It is purchased to yield 5% for the first 15 years and 4% thereafter. Calculate the (6 marks) amount for accumulation of discount for year 8. (d) You are given the following information in Table 1 about an investment account: 1 January | 1 March | 1ApriT 1 January Account value (Before deposit/withdrawal) 2017 2017 201720172018 102 20 100 108 118 130 X Deposit Withdrawal 12 Table 1 The time-weighted yield rate is 13.61% and the dollar-weighted yield rate is (7 marks) Total: 25 marks] 12.04%. Calculate T.

Explanation / Answer

ans. (3) :

Book value start of year 8 (23 years remaining) * yield rate - coupon; or
Book value end of year 8 (22 years remaining) - Book value start of year 8 (23 years remaining)

The first gives 7954.82*.05-300=97.74.
The second gives 8052.56-7954.82=97.74.

ans(4):

Based on the information on the time-weighted rate of return,

we have

1.1361 = 108/100 * 102/96 * 118/122 * 130/(118 + X) , and this gives X = 9.

Let us denote by Y the fraction of a year that the deposit of X = 9 was in the account. Using the information about the time-weighted rate of return, we get

0.1204 = (130-29 + 12 - 100) / 100-12 * 10/12 + 20 *9/12 + 9 *Y .

This gives Y = 1/3 and therefore,

T = September 1.

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