A 100,000 loan has an annual nominal interest rate of 8% convertible quarterly. The loan will be repaid with quarterly payments and the first payment is due three months from the date of the loan. For the first five years each payment will be 2500. All payments thereafter will be 5000 except for a final balloon payment, which will be less than 10,000.

Calculate the balloon payment

• 7920
• 8078
• 9056
• 9154
• 9237

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

Value at time 5 years:

[[math]] \begin{aligned} & 100,000(1.02)^{20}-2500 s_{\overline{200}|0.02} \\ & 87,851.32=5000 a_{\overline{m}|0.02} \end{aligned} [[/math]]

[math]m=21.86[/math], using the BA II Plus. Since we want a balloon payment, use [math]m=21[/math].

[[math]] 87,851.32=5000 a_{210.02}+B v^{21} [[/math]]

[math]\mathrm{B}=4236.70[/math], so balloon equals [math]5000+4236.70=9236.70[/math]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.