Respuesta :
Answer:
the interest rate that Sandy is getting is (C.) 15.10%
Explanation:
Given data
in 4 year cash pay (p1) = $2000
in 8 year cash pay (p2) = $3000
time period (t1) = 4 years
time period (t2) = 8 years
loan value = $2000
To find out
interest rate
solution
first we know amount will be paid in first 4 year is
$2000 [tex](1+r/100)^{12t}[/tex]
$2000 [tex](1+r/100)^{48}[/tex] ...................1
now we calculate the next payment will paid after 4 year i.e.
$2000 [tex](1+r/100)^{12t}[/tex] - $2000
$2000 [tex](1+r/100)^{48}[/tex] - $2000 ..................2
after full time period of payment total amount will be paid by equation 1 and 2 i.e.
$3000 = $2000 [tex](1+r/100)^{48}[/tex] ×$2000 [tex](1+r/100)^{48}[/tex] - $2000
$3000 = $2000 ( [tex](1+r/100)^{48}[/tex] × [tex](1+r/100)^{48}[/tex] - 1 ) .....3
now we have solve [tex](1+r/100)^{48}[/tex] this eqution
so we consider [tex](1+r/100)^{48}[/tex] = A
so new equation will be by equation 3
$3000/$2000 = ( A - 1 ) × A
3/2 = A² - A
solve this equation we get 2A² - 2 A - 3 = 0 so A = 1.823
now we compute A again in [tex](1+r/100)^{48}[/tex] = A
[tex](1+r/100)^{48}[/tex] = 1.823
so rate (r) = 1.258 % / month
and rate yearly = 1.258 ×12
the interest rate that Sandy is getting yearly 15.10 %
