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# A loan has a variable interest rate that fluctuates between 5% and 9%

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Math Expert
Joined: 02 Sep 2009
Posts: 51281
A loan has a variable interest rate that fluctuates between 5% and 9%  [#permalink]

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24 Jul 2018, 23:44
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:31) correct 18% (01:38) wrong based on 40 sessions

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A loan has a variable interest rate that fluctuates between 5% and 9% of the base payment per month. If base payments remain at $250 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? A.$262.50
B. $265.13 C.$272.50
D. $275.23 E.$286.13

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Posts: 7112
Re: A loan has a variable interest rate that fluctuates between 5% and 9%  [#permalink]

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25 Jul 2018, 00:23
Bunuel wrote:
A loan has a variable interest rate that fluctuates between 5% and 9% of the base payment per month. If base payments remain at $250 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? A.$262.50
B. $265.13 C.$272.50
D. $275.23 E.$286.13

so we take the MAX values..
so BASE payment = 250 and interest rate = 9%
so 250*1.09 but 1% on top = $$250*1.09*1.01$$

since you are looking at slight dispersed choices, we can approximate and find answer
9% ~ 10% so 10% of 250 = $$250*\frac{10}{100}=25$$
so slightly less than 275 add 1% to it so $$275+2.75 = 277.75$$
so our answer has to be closer and < 277
only D is left
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Re: A loan has a variable interest rate that fluctuates between 5% and 9%  [#permalink]

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25 Jul 2018, 18:25
1
Bunuel wrote:
A loan has a variable interest rate that fluctuates between 5% and 9% of the base payment per month. If base payments remain at $250 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? A.$262.50
B. $265.13 C.$272.50
D. $275.23 E.$286.13

Can someone explain this one to me using a different method or point out the error in my thinking?

Use max value of 9% interest to calculate base and then add 1% interest to that value

Base payment + Base interest + Additional interest = Total

250 + .09(250) + (.01(.09(250)) =250 + 22.5 + .225 = 272.725
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A loan has a variable interest rate that fluctuates between 5% and 9%  [#permalink]

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27 Jul 2018, 18:33
1
jch103020 wrote:
Bunuel wrote:
A loan has a variable interest rate that fluctuates between 5% and 9% of the base payment per month. If base payments remain at $250 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? A.$262.50
B. $265.13 C.$272.50
D. $275.23 E.$286.13

Can someone explain this one to me using a different method or point out the error in my thinking?

Use max value of 9% interest to calculate base and then add 1% interest to that value

Base payment + Base interest + Additional interest = Total

250 + .09(250) + (.01(.09(250)) =250 + 22.5 + .225 = 272.725

jch103020 , easy mistake.

The "additional interest" does not work because you are charging 1% on interest only:
(.09)(250) = $22.50, and ($22.50 *.01) = $0.225 The extra 1% should be charged on base + interest: 1.09(250) =$272.50

So either
Base payment + Base interest + Additional interest (1% on base payment PLUS base interest) = Total

250 + .09(250) + (.01*(1.09*(250)) = (250 + 22.5 + 2.725) = $275.225 OR Add your first two terms:$250 + $22.50 =$272.50
1% on that amount: (.01)($272.5) =$2.725
($250 +$22.50 + $2.725) =$275.225

If you think about multiplying decimals, it makes sense. (.01*.09) = .0009. You've charged 9/100th of a percent (.09%) on \$250

Hope that helps.
A loan has a variable interest rate that fluctuates between 5% and 9% &nbs [#permalink] 27 Jul 2018, 18:33
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