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

Reeves 2021-05-11 Answered
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

smallq9
Answered 2021-05-12 Author has 106 answers
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=12214.0310000=2214.03
Step 3
c) Hence, simple interest results in less total interest.

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