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This should be easy. I've been assured that this is correct, but I don't see how.

$\$40,000$ plus a $\$200.00$ administrative fee plus $3\%$ for four months on $\$40,200 = \$40,602$.

I think it should be $40,000 + 200 + (0.03 \times 40,200 \times 4) = 45,024$ Who is right?

lioness99a
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Jay Moché
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3 Answers3

1

Notice that

$$\frac{40602}{40200}=1.01,$$

corresponding to $4\cdot\dfrac{3}{12}\%$.

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    Shouldn't that be $1.03^{4/12}\approx1.00990$? – Servaes Feb 02 '20 at 20:08
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    Many thanks for the downvote. –  Feb 02 '20 at 20:10
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    @Servaes it simply shows it to be APR not APY. –  Feb 02 '20 at 20:13
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    @Servaes: using monthly compound interests would yield the value $40598.04\cdots$. Given the accuracy of the data, we obviously have simple interests. We have to infer from the loose question. –  Feb 02 '20 at 20:15
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    wrong monthly compounding gives 40603.51 ... –  Feb 02 '20 at 20:17
  • Thank you all for correcting me. – Jay Moché Feb 02 '20 at 20:17
  • 40200*(1+(3/1200))^4 %2 = 5197249281801/128000000 %*1. %3 = 40603.51001407031250000000000 it's stated nowhere therefore we can't assume. –  Feb 02 '20 at 20:19
  • @RoddyMacPhee: the information we have is $3%$, presumably yearly. Which can be understood as $0.25%$ monthly (simple interest) or $1.03^{1/12}-1=0.24662\cdots%$ monthly (compound interest). One can also understand $0.25%$ monthly (compound interest, $3.0416\cdots%$ yearly) but this is not really logical. Given the figures, how can one doubt $40200\times 1.01$ ?? –  Feb 02 '20 at 20:29
  • They are asking which is correct, not if it is correct ... –  Feb 02 '20 at 20:35
  • I neglected to add that it is annual percentage. – Jay Moché Feb 02 '20 at 20:35
  • @RoddyMacPhee: $(1+3%/12)^{12}\ne1+3%$. You should know that. –  Feb 02 '20 at 20:37
  • I do but that's how compounding goes if given APR. Otherwise you'd be wrong as APY gives a different rate. –  Feb 02 '20 at 20:50
  • @RoddyMacPhee: all three interpretations are possible. There is no doubt on the one that fits. –  Feb 02 '20 at 20:55
1

Explaining one of the comments a bit more... $3\%$ is the annual rate. Since we only have 4 months it is
$40,000 + 200 + (0.03 \times 40,200 \times 4/12) = 40,602 $

where $4/12$ is there because we only care about 4 out of the 12 months.

Cheese Cake
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shortmanikos
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0

I believe 3% is the annual rate. So, because we only have 4 months we get 4/12 or 1/3 of the year so the equation would be:

40,000+200+(0.03×40,200×1/3)=40,602

I hope this helped you understand this at least a little bit more.