Bethany needs to borrow $10,000. She can borrow the money at 5.5% simple interest for 4 yr or she can borrow at 5% with interest compounded continuously for 4 yr. a. How much total interest would Bethany pay at 5.5% simple interest?b. How much total interest would Bethany pay at 5% interest compounded continuously? c. Which option results in less total interest?

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Asked Dec 26, 2019
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Bethany needs to borrow $10,000. She can borrow the money at 5.5% simple interest for 4 yr or she can borrow at 5% with interest compounded continuously for 4 yr. 

a. How much total interest would Bethany pay at 5.5% simple interest?

b. How much total interest would Bethany pay at 5% interest compounded continuously? 

c. Which option results in less total interest?

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Expert Answer

Step 1

A. Simple interest for an amount P, at an interest rate of r (in decimals) per annum and for T years is given by:

Plugging the values:

Algebra homework question answer, step 1, image 1
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Step 2

B. Amount after continuous compounding for T years of principle P at an interest rate of r is given by:

Plugging the values:

So the interest is given by:

Algebra homework question answer, step 2, image 1
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Step 3

C. Hence, simple interest result...

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