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mezya [45]
3 years ago
14

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 t

he 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%
Mathematics
2 answers:
jok3333 [9.3K]3 years ago
5 0

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


Step-by-step 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[\frac{1-(1+r)^{-n}}{r}],\text{where r is the rate of interest per month}\\\\\Rightarrow3000=350[\frac{1-(1+r)^{-10}}{r}]\\\\\Rightarrow\frac{60}{7}=[\frac{1-(1+r)^{-10}}{r}]\\\\\Rightarrow\frac{60}{7}r=1-(1+r)^{-10}\\\\\Rightarrow\frac{60}{7}r=\frac{(1+r)^{10}-1}{(1+r)^{10}}\\\Rightarrow\frac{60}{7}r(1+r)^{10}=(1+r)^{10}-1\\\Rightarrow\frac{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%

nikklg [1K]3 years ago
3 0
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%
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