geometric sequence

• Jul 10th 2013, 04:25 AM
spacemenon
geometric sequence
Charles borrows $6000 for a new car.Compound intrest is charged on the loan at at a rate of 2% per month.Charles has to pay off the loan with 24 equal monthly payments.Calculate the value of each monthly payment. Any help is appreciiated the answer in text is 317.226 • Jul 10th 2013, 04:31 AM Prove It Re: geometric sequence I don't think using geometric sequences here is appropriate, as you are paying money on the amount owing, instead of interest just accumulating on what is owed. This is actually an annuity. I suggest looking up the annuities formula. • Jul 10th 2013, 07:38 AM Soroban Re: geometric sequence Hello, spacemenon! Are you expected to solve this with Geometric Sequences? That is an awesomely involved problem. Quote: Charles borrows$6000 for a new car.
Compound intrest is charged on the loan at at a rate of 2% per month.
Charles has to pay off the loan with 24 equal monthly payments.
Calculate the value of each monthly payment.

Textbook answer: 317.226 . ??

That is a strange answer.
First of all, it should be rounded to the nearest cent.
Second, it is inaccurate.

This is an Amortization problem.

Formula: . $A \;=\;P\frac{1(1+i)^n}{(1+i)^n-1}$

. . where: . $\begin{Bmatrix}A &=& \text{periodic payment} \\ P &=& \text{principal borrowed} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$

We have: . $P = 6000,\;i = 0.02,\;n = 24$

Hence: . $A \;=\;6000\,\frac{0.02(1.02)^{24}}{1.02^{24}-1} \;=\;317.2265835 \;\;{\color{blue}\approx\;317.227}$

Therefore: . $A \;=\;\317,23$
• Jul 11th 2013, 06:47 AM
spacemenon
Re: geometric sequence
you r right i gave the calculater answer text answer is 317.23