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If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%

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If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 19 Mar 2017, 07:04
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If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25% annual interest, which of the following is closest to the net interest rate for one year?

A. 6.9%
B. 6.8%
C. 6.6%
D. 6.4%
E. 6.2%

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Re: If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 19 Mar 2017, 07:48
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Bunuel wrote:
If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25% annual interest, which of the following is closest to the net interest rate for one year?

A. 6.9%
B. 6.8%
C. 6.6%
D. 6.4%
E. 6.2%


$2,000 at 5.25% annual interest
1-year's interest = 5.25% of $2000
= 0.0525 x $2000
= $105

$2,500 at 8.25% annual interest
1-year's interest = 8.25% of $2500
= 0.0825 x $2500
= $206.25

TOTAL interest = $105 + $206.25 = $311.25
TOTAL Investment = $2000 + $2500 = $4500

Net interest rate = (100)($311.25)/($4500)
≈ 0.691%

Answer: A

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Re: If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 20 Mar 2017, 03:28
Bunuel wrote:
If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25% annual interest, which of the following is closest to the net interest rate for one year?

A. 6.9%
B. 6.8%
C. 6.6%
D. 6.4%
E. 6.2%

we will equate the total interest. let the equivalent interest be x
2000*0.0525 + 2500* 0.0825 = 4500*x/100
105 + 206.25 = 45*x
or x = 6.9%

Option A
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If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 17 May 2017, 16:05
If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25% annual interest, which of the following is closest to the net interest rate for one year?

A. 6.9%
B. 6.8%
C. 6.6%
D. 6.4%
E. 6.2%

SI = PTR/100 (SI = Simple interest, P = Principal, T = Time, R = Rate of interest)
Simple interest for $2000 = \(\frac{2000*5.25*1}{100}\) = 105
Simple interest for $2500 = \(\frac{2500*8.25*1}{100}\) = 206.25
Total principal = 2000 + 2500 = 4500
Total interest = 105 + 206.25 = 311.25
Required Net Interest Rate = Total Interest x 100/Total Principal x Time = \(\frac{311.25*100}{4500*1}\) = 6.9%
Answer A...

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Re: If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 22 May 2017, 18:41
Bunuel wrote:
If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25% annual interest, which of the following is closest to the net interest rate for one year?

A. 6.9%
B. 6.8%
C. 6.6%
D. 6.4%
E. 6.2%


We can create the following weighted average equation:

[0.0525(2,000) + 0.0825(2,500)]/(2,000 + 2,500)

(105 + 206.25)/4,500

311.25/4,500 = 0.0691, which is about 6.9%.

Answer: A
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Re: If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 14 Nov 2017, 01:01
The amounts are in ratio 2000:2500 = 4:5

weighted average of interest is \((5.25*4+8.25*5)/9 = 62.25/9\), slightly less than 7
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Re: If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 04 Feb 2018, 06:12
mjana89 wrote:
The amounts are in ratio 2000:2500 = 4:5

weighted average of interest is \((5.25*4+8.25*5)/9 = 62.25/9\), slightly less than 7


I tried a variation of this method (alas after doing the sum in the normal way first :roll: )

Here goes my attempt to solve this quickly:

Data: 2k @5.25% and 2.5 @ 8.25%
Q1: what can i interpret quickly
Inference 1: the amount with higher interest is higher hence the overall interest will be greater than 5.25%
this doesnt help with reducing options

Q2: can i get more such data points that help me to reduce options.
inference 2: What if the amounts were equal, the avg return would be the average of the percentages
overall Rate of interest = i
(5.25 + 8.25)/2 < i

assuming interest as 2K @5.25% and 2K @ 8.25

=> i >6.75

Eliminate option 3, 4, and 5

Now what about the options 1 and 2 (all options are uncomfortably close)

Q3. What is the differential %

as we accounted for 2K @5.25% and 2K @ 8.25
we need to account for 500 @ 8.25 %

Differential interest = 500 * 8.25% = 41.25
this would translate into overall % as = 41.25*100/(2K + 2.5K)
=41.25/45
almost 1% but greater than 0.9% (this sucks as i now have 7.25%)


Q4 what can i correct now

realized that in Q2 base is not 4K but 4.5K hence overall rate will reduce
Recalculated avg interest = 2K (5.25 +8.25 ) / 4.5 = 2K (13.5)/4.5k = 6%

so overall would be slightly more than 6.9%

Finally, Phew
Will keep the weight method in mind
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Re: If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 04 Feb 2018, 06:30
Tried using weighted average method:

weight1 : weight2 = 2000 : 2500 = 4 : 5

5.25 (weight = 2000) <-------5--------> net interest <------4------->8.25 (weight = 2500)

so net interest rate = (5/9) * (8.25 - 5.25) + 5.25 = (5/9) * 3 + 5.25 = 1.667 + 5.25 = 6.9 approx (A)
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Re: If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%  [#permalink]

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New post 05 Feb 2018, 00:25
Bunuel wrote:
If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25% annual interest, which of the following is closest to the net interest rate for one year?

A. 6.9%
B. 6.8%
C. 6.6%
D. 6.4%
E. 6.2%


From the question we have,
Let r be the Annual Rate.
\(2,000*\frac{21}{400} + 2500*\frac{33}{400}= 4500*\frac{4r}{400}\)
\(r = 6.9167%\)
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Re: If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25% &nbs [#permalink] 05 Feb 2018, 00:25
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