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29 October, 00:45

You manage a pension fund that promises to pay out $10 million to its contributors in five years. You buy $7472582 worth of par-value bonds that make annual coupon payments of 6% and mature in five years. Right after you make the purchase, the interest rate on same-risk bonds decreases to 4.5%. If the rate does not change again and you reinvest the coupon payments that you receive in same-risk bonds, how much will you fall short of the money that you promised

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  1. 29 October, 01:04
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    Shortfall of money = $74,598

    Explanation:

    As per the data given in the question,

    Par value of bond = $7,472,582

    To determine the future value of annual coupon payments received, we will use FV of annuity's formula

    FV of Annuity = P [ (1 + r) ^n - 1 : r]

    where,

    P = Periodic payment

    r = interest rate

    n = Time period

    here P = 6% of $7,472,582 = $448,354.92

    r = 4.50%

    n = 5 years

    FV of Annuity = $448,354.92 * [ (1 + 4.50%) ^5 - 1) : 4.50%]

    =$2,452,820

    Shortfall at the end of 5 years is

    = $10,000,000 - $7,472,582 - $2,452,820

    = $74,598
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