A man purchases a $2000 diamond ring for
a down payment of $200 and monthly installments of $88 for
2 years. Assuming that interest is compounded monthly, what
interest rate is he paying?

Question

A man purchases a $2000 diamond ring for
a down payment of $200 and monthly installments of $88 for
2 years. Assuming that interest is compounded monthly, what
interest rate is he paying?

anonymous · Answer

.0627 or 6.27% annually

rock_mit182 · Answer

well is awesome "the answer" but i need more step through the problem

rock_mit182 · Answer

could anybody explain to me how to solve this ?

radar · Answer

Do you know the compounding interest formula?  That might be a good starting point.  The formula I have is A = P(1 + r/n)^(nt)
where n would be 12 for this problem.  You would need to solve for r

rock_mit182 · Answer

n is always the amount of time ?

radar · Answer

n is the number of compoundings per year
t is the number of years in this case t = 2

rock_mit182 · Answer

p = principle amount ?

radar · Answer

n=12
t=2
P= principal
A= Balance

radar · Answer

You may want to use a google and find a financial calculator.  What kind of formula does your reference text suggest?

rock_mit182 · Answer

$$A = 2*10^{3}(1+ \frac{ r }{ 12 })^{12*2} $$

rock_mit182 · Answer

well there are three

rock_mit182 · Answer

If a loan Ap is to be repaid in n regular equal payments with interest rate i per
time period, then the size R of each payment is given by

rock_mit182 · Answer

$$R =\frac{ iA _{p} }{ 1-(1+i)^{-n} }$$

rock_mit182 · Answer

i can use  that one ?

anonymous · Answer

that's the formula i used, however that's annual payment so u have to divide the r by 12, solving for i is always tricky algebraically so i just use excel

radar · Answer

Don't forget he did make a 200 dollar down payment and the amount would be $1800.00

rock_mit182 · Answer

well let me see

rock_mit182 · Answer

$$\frac{ 1- (1+i)^{-n}R }{ A } =i$$

rock_mit182 · Answer

$$\frac{ 1-R }{a(1+i)^{n}  } = i $$

radar · Answer

The calculator I found states the interest rate is 15.845%  Need to look further into that.

rock_mit182 · Answer

i guess i did something wrong already

anonymous · Answer

radar did u use pmt function on excel?

radar · Answer

Well it might be that when you consider 24 payments of $88 is $2,112.00 which is $312.00 of interest over a 24 month period.

anonymous · Answer

right but the payments are discounted at different times since you pay monthly

radar · Answer

No I am using this calculator, I will send the link http://www.mycalculators.com/ca/loancalcm.html

rock_mit182 · Answer

Can I calculate this on wolfram alpha ?

anonymous · Answer

yeesh im a moron i thought the payment was 80 not 88

anonymous · Answer

radar's answer is right

radar · Answer

The original formula I provided a balance but not the interest rate when the monthly payment is given.  So it needs to be modified somehow that when the payment is given you can figure out the interest rate.  I need to ponder this....

rock_mit182 · Answer

guys the true I'm not good at all on this kind of math

rock_mit182 · Answer

I thought that i could figure out this by myself not with a calculator

rock_mit182 · Answer

I thought that i could figuere out this by myself not with a calculator

rock_mit182 · Answer

Anyway thanks a lot! to both of you