Question

Luke let a friend borrow $5,000 that was to be paid back in a single payment after three year period. Luke gave his friend two financing options shown below. The best choice for Luke's friend is _______

Option A: 10% per year simple interest

Option B: 4.5% per half-year, compounded continuously

a) Option A because it saves approximately $771 in interest

b) Option A because it saves approximately $50 in interest

c) Option A because it saves approximately $91 in interest

d) Option A because it saves approximately $117 in interest

e) Option B because it saves approximately $145 in interest

f) Option B because it saves approximately $55 in interest

g) Option B because it saves approximately $72 in interest   

h) Option B because it saves approximately $33 in interest

i) Either option because they result in the same single payment

j) Not enough information is given to make a choice

Answer 1

Option A

I = 10% simple interest

t =3 yrs

P = 5000

Simple interest = P*R*T

simple interest = 5000 * 0.1 * 3 = 1500

Option B

I = 4.5% per half year compounded continously

Effective half year interest rate = e^r -1 = e^0.045 - 1 = 1.04602786 - 1 = 0.04602786

F = P*(1+I)^t

Here t = 6 half yr periods

F = 5000*(1+0.04603)^6

= 5000*1.309980

= 6549.90 = 6550

Interest = 6550 - 5000 = 1550

Saving in interest payment if option A is selected = 1550 - 1500 = 50

so correct answer is b) Option A because it saves approximately $50 in interest