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.

Question

Business

Crystal Baird

4 July, 16:56

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.

+3

Answers (1)

Know the Answer?

Essence Butler · Answer 1

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