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After getting a great job from your prestigious CSM degree, you are shopping for a $300,000, 30-year home loan.The monthly payment is m(r) = (300000 r /12) / 1 − (1 + r 12 ) −360,where r is the annual interest rate. Current interest rates are anywhere between 2% (r = 0.02) and 5% (r = 0.05), depending on credit.(a) Use the Intermediate Value Theorem to show that there is an interest rate between 2 and 5 percent that allows you to make a monthly payment of $1250. Show that all conditions of the theorem are met and correctly state the conclusion in context. Be specific about the intervals for this problem; don’t just state IVT generally.

Question

After getting a great job from your prestigious CSM degree, you are shopping for a $300,000, 30-year home loan.

The monthly payment is m(r) = (300000 r /12) / 1 − (1 + r 12 ) −360

,where r is the annual interest rate. Current interest rates are anywhere between 2% (r = 0.02) and 5% (r = 0.05), depending on credit.

(a) Use the Intermediate Value Theorem to show that there is an interest rate between 2 and 5 percent that allows you to make a monthly payment of $1250. Show that all conditions of the theorem are met and correctly state the conclusion in context. Be specific about the intervals for this problem; don’t just state IVT generally.

check_circleAnswer
Step 1

Given that the monthly payment is

300000
12
-360
m(r)
1 -1
12
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300000 12 -360 m(r) 1 -1 12

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Step 2

The interest rate r must lie between 0.02 and 0.05 for a monthly payment of $1250.

300000스
12
1250
-360
1-1+
12
-360
300000
1-1+
12
125012
-360
1-1+
=240
12
12
r 0.03
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300000스 12 1250 -360 1-1+ 12 -360 300000 1-1+ 12 125012 -360 1-1+ =240 12 12 r 0.03

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Step 3

...

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