# 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
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?

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.