A loan is negotiated with the 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 negotiated 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.

Taking the present time as t= 0, the scheduled loan repayments is,

0 ---->

1 -----> $8,000

2 -----> $9,000

3 ----->

4 -----> $20,000

According to the method of equated time,Tis a dollar-weighted average of thepayment times; that is, with time measured in years,

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

= ( 106,000 /37,000 ) ≈ 2.864864865 ≈ 2.86487.

The equation of value at time t= 0 is,

=

wherev= (1.05), Solving for T gives:

T =

=2.82480766.

answer; ///the name of the central bank of the united states is called; ///the federal reserve known as the federal

dunce cap 4life lollolol