Andy Z. opens a sketchy rent to own store where his catch phrase is, “I’ll divide your cost by 20 and you can pay that amount for 24 months.” In the fine print it says that the first payment is due at purchase and every subsequent payment is due at monthly intervals after that.

What are Andy’s store’s customers paying on their loans?

• .218
• .0012
• .01655
• .268
• .182

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Solution: A

Present value = x

Payments = x/20 or .05x for 24 months

Interest rate = i per month

To calculate annual interest rate we must first set up the equation for this annuity:

[[math]] \begin{aligned} & \mathrm{x}=.05x \ddot{a }_{\overline{24}|i} \\ & 1=.05 \ddot{a}_{\overline{24}|i} \\ & 20=\left(\left(1-\mathrm{v}^{24}\right) / \mathrm{d}\right) \\ & 20 \mathrm{~d}=1-(1 / 1+\mathrm{i})^{24} \\ & \mathrm{i}=.01655 \quad \text { monthly interest rate }\end{aligned} [[/math]]

To calculate the yearly interest rate: (1 + .01655)¹² – 1 = .218

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.