# 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.

Step 1

Given that the monthly payment is

Step 2

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

Step 3

...

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