This question has been solved here: Could someone please check my math?
- Lliam
**Funny side note: While typing this up, as a question, half way through I think I figured it out, which is why this is now a "check my math" post**
Hello,
I'm currently getting my grade 11 college math (Functions and Applications, MCF3M) through a learn from home program. Unfortunately I ran into a little trouble with this problem, which had me stumped . I would be very thankful to anyone who could check my math
By the way, sorry if this is not a question involving equivalent rates but it's the title of the section this is in, in my book, and I wasn't sure what it is considered. :P
Nader plans to buy a used car. He can afford to pay $280 at the end of each month for three years. The best interest rate he can find is 9.8%/a, compounded monthly. For this interest rate, the most he could spend on a vehicle is $8702.85.
Determine the amount he could spend on the purchase of a car if the interest rate is 9.8%/compounded annually.
First of all, I understand the first part about him being able to spend $8702.85. I know this can be figured out using the present value formula:
PV=R[1-(1+i)^-n]/i
=$280[1-(1+[.098/12])^-36]/(.098/12)
=8702.849629
Which, rounded, gives you $8702.85
And I think this is how you figure out the question (though like I said I'm unsure):
1) Find the (monthly?) interest rate (of the compounded annually plan?)
(1+i)^12=(1+[.098/12])
(1+i)^12=(1.008166667)
1+i=12√1.008166667
1+i=1.000678021
i=1.000678021-1
i=.000678021
2)Use this new interest rate in the present value formula used earlier
PV=R[1-(1+i)^-n]/i
=280[1-(1+.000678021)^-36]/.000678021
=9954.641382
Which, rounded, gives you $9954.64
Therefore Nate could spend $9954.64 on the purchase of a car.
*NOTE: I am also unsure whether I should be using the future value formula in step 2 instead of the present value formula.*
Like I said, if someone could look this over and tell me if I did it right or what I did wrong I would be EXTREMELY thankful!
- Lliam
This question has been solved here: Could someone please check my math?
- Lliam