 # 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 $5.5\mathrm{%}$ simple interest for 4 yr or she can borrow at $5\mathrm{%}$ with interest compounded continuously for 4 yr.
a) How much total interest would Bethany pay at $5.5\mathrm{%}$ simple interest?
b) How much total interest would Bethany pay at $5$ interest compounded continuously?
c) Which option results in less total interest?
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it smallq9
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:
$I=PTr$
$I=\left(10000\right)\left(4\right)\left(0.055\right)$
$I=2200$
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:
$A=P{e}^{rT}$
$A=\left(10000\right){e}^{\left(0.05\right)\left(4\right)}$
$A=\left(10000\right){e}^{0.2}$
$A=\left(10000\right)\left(1.221402\right)$
$A=12214.03$
$I=12214.03-10000=2214.03$
Step 3
c) Hence, simple interest results in less total interest.

We have step-by-step solutions for your answer!