*FDP 5th ed-Chapt 3 quest 4. Car loan offered at 8% annual

[estamand]

A car loan is offered at 8% annual interest, compounded annually. After the first year, the interest due is $240. What is the principal on the loan?

The answer explanation states: $3,000. Although this looks like an interest problem, you can think of it as a percent change problem. The percent change is 8%, and the change in value is $240. 8/100=240/x so 8x=24,000 and x=3,000.

Here is my question:
I understand how to solve this problem the above way. However, I was trying to see if I could solve this problem using the Compound Interest Rate formula:
Compound Interest is $240= P(1+r/n)^nt, where t=1yr, r=8% and n=1. So 240=P(1+.08)^1, 240=P(1.08), thus P=240/1.08=$222.22.
However, this is an incorrect answer (since P=$3000).
Could someone pretty please show me the errors of my way? I greatly appreciate it.

[RonPurewal]

Hi,
Per the forum rules, please type out the complete question. If there are answer choices, include those, too.
* We (moderators) don't always have the guides available when we're posting on the forum.
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Also, please read the forum rules (= first post in every folder) before posting.

Thanks.

[estamand]

Thank you Ron. I edited my original post. Thank you.

[RonPurewal]

You wrote:

Compound Interest is $240= P(1+r/n)^nt

This is incorrect.

The formula you've written here (P(1+r/n)^nt) is for the principal AND the accumulated interest. (You can figure this out by using common sense: it's "P" times a number that is more than 1, so, at any point after time zero, it's always greater than "P".)

So, if you started with P and accumulated $240 in interest, you'd have (P + 240).
Therefore, instead of 1.08P = 240, your equation should be 1.08P = P + 240.

[RonPurewal]

In any case, this is a strange problem, because it describes a car loan on which no payments are made for an entire year. Such loans don't exist, at least not in the United States.

I'll submit this problem for editing, since word problems should reflect reasonable real-world situations.

[estamand]

Thank you Ron. Yes, P time a number bigger than 1 should be bigger than $240 but I was not sure of how to rectify it. Thank you. And yes, I would love to have a car lease with only 1 payment made per year :) Thank you again.

[jnelson0612]

Thanks Ron!

[coolparthi]

What a strange coincidence. I ran into the same issue
Since this is only for 1 year, i used a Simple Interest formula which is Simple Interst = PNR/100.
But you should also be able to use a Compound Interest formula but found that it is my misinterpretation.
This is wrong: Interest = P(1+r/100)^nt
This is correct: Amount = P(1+r/100)^nt
in this example, Amount = 240 + P which implies
240 + P = P(108/100).

Thanks!

[RonPurewal]

coolparthi, are you asking a question? If so, I can't tell what it is.

"Simple interest" and "compound interest for 1 time period" are always the same. The effects of compounding aren't felt until the second time interest is compounded (since that's the first time interest is calculated on an amount greater than the original).