Question

16. 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. 3.6%
C. 63%
D. 36%

Answer 1

Answer: D is the correct option. The extra cost paid by taking this deal is equivalent to the actual yearly rate of interest=36%

Explanation:

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

As John made an agreement with the dealer to put $1,500 down payment

Therefore the present value of annuity (PV)=$4500-$1500=$3000

with periodic payment=$350 , time =10 months

Using formula for present value of annuity, we get

`PV=P[(1-(1+r)^(-n))/(r)],\text{where r is the rate of interest per month}\\\\\Rightarrow3000=350[(1-(1+r)^(-10))/(r)]\\\\\Rightarrow(60)/(7)=[(1-(1+r)^(-10))/(r)]\\\\\Rightarrow(60)/(7)r=1-(1+r)^(-10)\\\\\Rightarrow(60)/(7)r=((1+r)^(10)-1)/((1+r)^(10))\\\Rightarrow(60)/(7)r(1+r)^(10)=(1+r)^(10)-1\\\Rightarrow(60)/(7)r(1+r)^(10)-(1+r)^(10)+1=0`

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

Therefore, the actual yearly rate of interest= 12×3%=36%

Answer 2

10*350= 3500
Total amount paid- 1500+3500= 5000
So an amount of $5000 was paid to cover the cost of $4500 within the 10 month period.

So you answer is A. 33%