Question

Jake has four options for financing a $4,000 loan. The details of each option are shown in the table.

Annual Interest Rate Compounding Period Term
Option 1 8% monthly 3 years
Option 2 6% monthly 3 years
Option 3 8% quarterly 42 months
Option 4 10% biannually 2 years
He chooses the option in which he pays the least in interest.

Which option does he choose?

(1 point)
Responses

Option 4
Option 4

Option 3
Option 3

Option 2
Option 2

Option 1
Option 1

Answer 1

Compute the accumulated amount A = 4000(1 + r/m)^(m t) and interest = A − 4000 for each option (t in years).

Option 1: r=0.08, m=12, t=3
A1 = 4000(1 + 0.08/12)^(36) ≈ 4000(1.270234) ≈ 5080.94 → interest ≈ 1080.94

Option 2: r=0.06, m=12, t=3
A2 = 4000(1 + 0.06/12)^(36) ≈ 4000(1.196532) ≈ 4786.13 → interest ≈ 786.13

Option 3: r=0.08, m=4, t=42/12=3.5
A3 = 4000(1 + 0.08/4)^(14) = 4000(1.02)^{14} ≈ 4000(1.31946) ≈ 5277.84 → interest ≈ 1277.84

Option 4: r=0.10, m=2, t=2
A4 = 4000(1 + 0.10/2)^{4} = 4000(1.05)^{4} ≈ 4000(1.215506) ≈ 4862.02 → interest ≈ 862.02

Least interest is Option 2.