Answer:
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,
[tex](37,000v)^{t}[/tex]= [tex]8,000v + 9,000v^{2} + 20,000v^{4}[/tex]
wherev= (1.05)[tex]^{-1}[/tex], Solving for T gives:
T = [tex]ln\frac{(\frac{8}{37}v + \frac{9}{37}v^{2} + \frac{20}{37}v^{4}}{ln(v)}[/tex]
=2.82480766.
