# 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.

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

This is an Amortization problem.

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

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

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

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

Therefore: .$\displaystyle 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