You have two loans, for 2 years each. The total interest for the two loans is $138. On the first loan, you pay 7.5% simple interest on a principal of $800. On the second loan, you pay 3% simple interest. What is the principal for the second loan?

Hi there! Interest on the first loan is 800×.075×2=120. The interest on the second loan is 138-120=18. Now, we have to use the simple interest formula. 18=P×.03×2=300. Therefore, the answer is $300.

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ApusApus ApusApus · Answer 2 · 2019-03-15T05:58:24+01:00

Answer:

$300

Step-by-step explanation:

We are told that you have two loans, for 2 years each. The total interest for the two loans is $138. On the first loan, you pay 7.5% simple interest on a principal of $800.

Let us find the amount of interest for 1st loan.

[tex]I=Prt[/tex], where,

I = Amount of interest,

P = Principal amount,

r = Interest rate in decimal form,

t = Time

Let us convert our given rate for 1st loan in decimal form

[tex]7.5\%=\frac{7.5}{100}=0.075[/tex]

[tex]I=\$800*0.075*2[/tex]

[tex]I=\$800*0.15[/tex]

[tex]I=\$120[/tex]

Now let us find the amount interest for 2nd loan.

[tex]\text{Amount of interest for 2nd loan}=\$138-\$120[/tex]

[tex]\text{Amount of interest for 2nd loan}=\$18[/tex]

Let us convert our given rate for 2nd loan in decimal form

[tex]3\%=\frac{3}{100}=0.03[/tex]

Upon substituting our given values for 2nd loan in interest formula we will get,

[tex]\$18=P*0.03*2[/tex]

[tex]\$18=P*0.06[/tex]

[tex]\frac{\$18}{0.06}=\frac{P*0.06}{0.06}[/tex]

[tex]\$300=P[/tex]

Therefore, the principal amount for the 2nd loan is $300.