SOA Exam FM Sample Question 388
Study guide: Exam FM-2
A restaurant owner takes out a 120-month loan of 10,000 today. To pay off the loan, the owner will make end-of-month payments of P for each of the first 30 months, 1.1P for each of the next 40 months, and 1.2P for each of the final 50 months.
The monthly payments are based on an annual nominal interest rate of 6% compounded monthly.
Determine which one of the following is an equation of value that can be used to calculate P.
- A)
10{,}000 = P\ddot{a}_{\overline{30}|0.005} + 1.1P\ddot{a}_{\overline{40}|0.005} + 1.2P\ddot{a}_{\overline{50}|0.005} - B)
10{,}000 = Pa_{\overline{30}|0.005} + 1.1Pa_{\overline{40}|0.005} + 1.2Pa_{\overline{50}|0.005} - C)
10{,}000 = Pa_{\overline{30}|0.005} + (1.005)^{-30}\left(1.1Pa_{\overline{40}|0.005}\right) + (1.005)^{-40}\left(1.2Pa_{\overline{50}|0.005}\right) - D)
10{,}000 = P\ddot{a}_{\overline{30}|0.005} + (1.005)^{-30}\left(1.1P\ddot{a}_{\overline{40}|0.005}\right) + (1.005)^{-70}\left(1.2P\ddot{a}_{\overline{50}|0.005}\right) - E)
10{,}000 = Pa_{\overline{30}|0.005} + (1.005)^{-30}\left(1.1Pa_{\overline{40}|0.005}\right) + (1.005)^{-70}\left(1.2Pa_{\overline{50}|0.005}\right)
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