Discounting and Interest

Question

The amount of interest earned on A for one year is 336, while the equivalent amount of discount is 300. Find A.

Correct answer: $A=2800$

My work: From the interest, I get that $A(1+i)-A = 336 \iff Ai = 336$

However, I'm not sure how to interpret the discount part. It's clearly not what I interpreted it as, which was

$A-A\nu = 300 \iff A - A\frac{1}{1-d} = 300 \iff A-A(1+i) = 300 \iff -Ai = 300?$

The discount, as stated https://math.stackexchange.com/questions/264230/two-questions-about-rate-of-discount should be interpreted as $(A-300)(i+1)=A$. You have gotten the other part right. Now you just need to solve the simultaneous equation for $i$ and what you need to find, $A$. — JC12, Jul 15 '20 at 02:19
yes, I've seen that post but I didn't understand where that equation came from, so I posted the question — MinYoung Kim, Jul 15 '20 at 02:23

score 1 · Accepted Answer · answered Jul 15 '20 at 02:27

1

HINT: you have two equations. If we set $k=r+1$, where $r$ is the rate of interest, the first equation is $Ak-A=336$, the second is $ A- A/k=300$. Now solve the system.

answered Jul 15 '20 at 02:27

Anatoly

17,079

So the equation $A-A/k$ is where $A/k$ is the discounted, present value of an assumed future amount $A$? – MinYoung Kim Jul 15 '20 at 02:31
1

Yes, you are right. – Anatoly Jul 15 '20 at 02:35

Discounting and Interest

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