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Stuart pays back two student loans over a 4-yr period. One loan charges the equivalent of 3% simple interestand the other charges the equivalent of 5.5% simple interest. If the total amount borrowed was $32,000 andthe total amount of interest paid after 4 yr is $4,640, find the amount borrowed from each loan.a. 8,000 at 3% and 24,000 at 5.5%b. 11,000 at 3% and 21,000 at 5.5%c. 21,000 at 3% and 11,000 at 5.5%d. 24,000 at 3% and 8,000 at 5.5%

Answer :

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Answer:

d. 24,000 at 3% and 8,000 at 5.5%

Step-by-step explanation:

Let the principal for the 3% loan be [tex]P_a[/tex] and that for the 5.5% loan be [tex]P_b[/tex]. Let their respective interests be [tex]I_a[/tex] and [tex]I_b[/tex].

Then

[tex]I_a=P_a\times3\%\times4=0.12P_a[/tex]

[tex]I_b=P_b\times5.5\%\times4=0.22P_b[/tex]

From the question, the sum of the interests is 4640.

[tex]I_a + I_b = 4640[/tex]

[tex]0.12P_a + 0.22P_b = 4640[/tex]

Also, the total amount borrowed is 32000.

[tex]P_a + P_b = 32000[/tex]

To solve the last two equations simultaneously, multiply the second by 0.12 and subtract from the first (this eliminates [tex]P_a[/tex]).

[tex]0.10P_b = 800[/tex]

[tex]P_b = 8000[/tex]

From [tex]P_a + P_b = 32000[/tex],

[tex]P_a = 32000 - P_b = 32000-8000 = 24000[/tex]

Hence, $24,000 was borrowed at 3% and $8,000 was borrowed at 5.5%.

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