Question

Help please!

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. 33% B. 36% C. 3.6% D. 63%

Answer 1

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,

`4500-1500=\$3000`

We know that,

`\text{PV of annuity}=P[(1-(1+r)^(-n))/(r)]`

`PV\ of\ annuity=3000,\\\\P=350,\\\\r = x%\ monthly\\\\n=10\ months`

Putting the values,

`\Rightarrow 3000=350[(1-(1+x)^(-10))/(x)]`

`\Rightarrow (3000)/(350)=[(1-(1+x)^(-10))/(x)]`

`\Rightarrow (60)/(7)x=1-(1+x)^(-10)`

`\Rightarrow (1+x)^(-10)+(60)/(7)x-1=0`

Using calculator we get,

`\Rightarrow x=0.0291=2.91\% \approx 3\%`

Therefore, annual interest will be,

`=12* x=12 * 3=36\%`

Answer 2

Answer: option A. 33%

Step-by-step explanation:

1) Purchase price: $4500

2) Payments:

down: $1500
monthly: $350 * 10 = 3500

Total payments = $1500 + $3500 = $5000

3) Difference: $5000 - $3500 = $1500 = extra cost

4) Percent extra cost = (difference / purchase price) * 100 = ($1500/$4500)*100 = 33.3%