SOA Exam FM Sample Question 418
Study guide: Exam FM-2
A credit card charges an annual continuously compounded interest rate of 18%, plus a fee of 20 at the end of each year. These fees accrue interest once they are charged.
A borrower, upon receiving the credit card, immediately purchased a piano for 1500 with the card.
The borrower then made a payment of X at the end of every month. At the beginning of the third year, the borrower's credit card balance was 200.
Determine which of the following is an equation of value that can be used to solve for X.
- A)
1500 + 20e^{-0.18} + 20e^{-0.36} - X\sum_{k=1}^{24} e^{-0.015k} = 200e^{-0.36} - B)
1500 + 20e^{-0.18} + 20e^{-0.36} - X\sum_{k=1}^{24} e^{-0.015k} = 200 - C)
1500 + 20e^{0.18} + 20e^{0.36} - X\sum_{k=1}^{24} e^{0.015k} = 200e^{0.36} - D)
1500 + \dfrac{20}{1.18} + \dfrac{20}{(1.18)^{2}} - X\sum_{k=1}^{24} \dfrac{20}{(1.18)^{\frac{k}{12}}} = \dfrac{200}{(1.18)^{2}} - E)
1500 + \dfrac{20}{1.18} + \dfrac{20}{(1.18)^{2}} - X\sum_{k=1}^{24} \dfrac{20}{(1.18)^{\frac{k}{12}}} = 200
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