Answer:
Loan A is the cheapest.
Step-by-step explanation:
The different loan plans are showed in the image attached.
Loan A: 12 months of duration with 9.50%.
Loan B: 24 months of duration with 8.75%.
Loan C: 36 months of duration with 7.75%.
Loan D: 48 months of duration with 6.60%.
Now, all loans are compouneded monthly. Let's the compound interest formula
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Loan A:
[tex]A=2500(1+\frac{0.095}{12} )^{12(1)}\\A=2,748.12[/tex]
Loan B:
[tex]A=2500(1+\frac{0.095}{24} )^{24(2)} \\A=2500(1.004)^{48}\\ A=3,028.02[/tex]
Loan C:
[tex]A=2500(1+\frac{0.095}{36} )^{36(3)} \\A=2500(1.003)^{108}\\ A=3,454.94[/tex]
Loan D:
[tex]A=2500(1+\frac{0.095}{48} )^{48(4)}\\ A=2500(1.002)^{192}\\ A=3,668.95[/tex]
Now, if you compare, you will observe that Loan A offer the cheapest result for Judy.
Therefore, Judy should use the Loan A plan.
