Question

Bethany needs to borrow $10,000. She can borrow the money at 6% simple interest for 5 yr or she can borrow at 5% with interest compounded continuously for 5 yr.
a. How much total interest would Bethany pay at 6% simple interest?
b. How much total interest would Bethany pay at 5% interest compounded continuously?
c. Which option results in less total interest?

Answer 1

Answer:

a. $3000

b. 2840.25

c. compounded continuously

Explanation:

a. principal amount,  p = $10000

Interest rate in the case of simple interest = 6%

Time, t = 5 years

Interest amount = Prt

Interest amount = 10000 x 6% x 5 = $3000

b. principal amount,  p = $10000

Interest rate, r = 5%

Time, t = 5 years

Interest amount = Pe^(rt) - P

Interest amount = 10000 (2.71)^(5% x 5) - 10000

Interest amount = 2840.25

c. Compounded continuously has a lower interest amount.