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Complex interest rate problem
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theboyleman32
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GMATGuruNY
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This is a MIXTURE problem.Loan X has a principal of $10,000x and a yearly simple interest rate of 4%. Loan Y has a principal of $10,0000y and a yearly simple interest rate of 8%. Loans X and Y will be consolidated to form Loan Z with a principal of $[10,000x + 10,000y and a yearly simple interest rate of r%, where r = (4x +8y)/x+y. In the table, select a value for X and a value for Y corresponding to a yearly simple interest rate of 5% for the consolidated load. Make only two selections:
21
32
51
64
81
96
A 4% loan (X) is being combined with an 8% loan (Y) to form a CONSOLIDATED loan of 5%.
To solve, we can use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for X and Y (4% and 8%) on the ends and the percentage for the mixture (5%) in the middle.
X 4%-----------5%-----------8% Y
Step 2: Calculate the distances between the percentages.
X 4%-----1-----5%-----3-----8% Y
Step 3: Determine the ratio in the mixture.
The required ratio of X to Y is the RECIPROCAL of the distances in red.
X:Y = 3:1.
Only X=96 and Y=32 yield the required ratio of 3:1.
For two similar problems, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
