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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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?

smallq9 · Accepted 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:  I=PTr  I=(10000)(4)(0.055)  I=2200  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:  A=PerT  A=(10000)e(0.05)(4)  A=(10000)e0.2  A=(10000)(1.221402)  A=12214.03  I=12214.03−10000=2214.03  Step 3  c) Hence, simple interest results in less total interest.

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 continuo

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