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25 December, 21:44

A loan is negotiated with a lender agreeing to accept $8, 000 after one year, $9, 000 after two years, and $20, 000 after four years in full repayment of the loan. The loan is renegotiated so that the borrower makes a single payment of $37,000 at time T and this results in the same total present value of payments when calculated using an annual effective rate of 5%.

Estimate T using the method of equated time. Also find T exactly.

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  1. 25 December, 22:05
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    T = 2.8647

    Explanation:

    Present time t = 0,

    According to the method of equated time:

    Tis a dollar-weighted average of the payment times with time measured in years

    Hence:

    T = ($8,000/$37,000) 1 + ($9,000/$37,000) 2 + ($20,000/$37,000) 4

    T = 0.2162 + 0.4864+2.1621

    T = 2.8647
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