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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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abiolataiwo2015

Answer:

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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