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

Question

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%

BrentGMATPrepNow · Answer

$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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KrishnakumarKA1 · Answer

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

sashiim20 · Answer

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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ScottTargetTestPrep · Answer

We can create the following weighted average equation:

/(2,000 + 2,500)

(105 + 206.25)/4,500

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

Answer: A

mjana89 · Answer

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

MT1988 · Answer

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

) 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

hellosanthosh2k2 · Answer

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)

rahul16singh28 · Answer

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%

bumpbot · Answer

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

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