Answer-
The extra cost paid by taking this deal is equivalent to actual yearly rate of interest 36%
Solution-
Price of truck = $4500
John made a down payment of $1500, so the present value of annuity will be,
[tex]4500-1500=\$3000[/tex]
We know that,
[tex]\text{PV of annuity}=P[\frac{1-(1+r)^{-n}}{r}][/tex]
[tex]PV\ of\ annuity=3000,\\\\P=350,\\\\r = x%\ monthly\\\\n=10\ months[/tex]
Putting the values,
[tex]\Rightarrow 3000=350[\dfrac{1-(1+x)^{-10}}{x}][/tex]
[tex]\Rightarrow \dfrac{3000}{350}=[\dfrac{1-(1+x)^{-10}}{x}][/tex]
[tex]\Rightarrow \dfrac{60}{7}x=1-(1+x)^{-10}[/tex]
[tex]\Rightarrow (1+x)^{-10}+\frac{60}{7}x-1=0[/tex]
Using calculator we get,
[tex]\Rightarrow x=0.0291=2.91\% \approx 3\%[/tex]
Therefore, annual interest will be,
[tex]=12\times x=12 \times 3=36\%[/tex]
