Question

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

Decimals
ANSWERED
asked 2021-05-11
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?

Expert Answers (1)

2021-05-12
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:
\(A=Pe^{rT}\)
\(A=(10000)e^{(0.05)(4)}\)
\(A=(10000)e^{0.2}\)
\(A=(10000)(1.221402)\)
\(A=12214.03\)
\(I=12214.03-10000=2214.03\)
Step 3
c) Hence, simple interest results in less total interest.
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