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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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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%
[Reveal] Spoiler: OA

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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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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, 02:28
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, 15:05
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, 17:41
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, 00:01
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] 14 Nov 2017, 00:01
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If Carter invested $2,000 at 5.25% annual interest and $2,500 at 8.25%

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