Question

John bought a used truck for $4,500. He made an agreement with the dealer to put $1,500 down and make payments of $350 for the next 10 months. The extra cost paid by taking this deal is equivalent to what actual yearly rate of interest? A. 36% B. 33% C. 63% D. 3.6%

Answer 1

Answer: 36%

Step-by-step explanation:

Given: Cost Price of used truck bought by John=$4500

Present value of annuity (PV)=$4500-$1500=$3000

with periodic payment=$350 , time (n) =10 months

The formula for present value of annuity is given by,

$PV=P\frac{1-(1+r)^{-n}}{r}\\\Rightarrow\ 3000=350\frac{1-(1+r)^{-10}}{r}\\\Rightarrow\ \frac{1-(1+r)^{-10}}{r}=\frac{60}{7}\\\Rightarrow\ \frac{60}{7}r(r+1)^{10}-(1+r)^{10}+1=0$

By solving the equation with the help of calculator ,we get r=0.029≈0.03=3%

hence, the actual yearly rate of interest= $12\times3</strong></p><p><strong>\%$=36%