107k views
0 votes
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%

User Leshane
by
8.5k points

2 Answers

4 votes

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%

User Ishaq
by
7.7k points
2 votes
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%
User Orakull
by
7.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories