SOA Exam FM Sample Question 265
Study guide: Exam FM-2
Consider two loans. Loan A has an initial principal of P_0 and an annual nominal interest rate of i, convertible monthly. Loan B also has an annual nominal interest rate of i, but the interest is convertible daily.
At the end of the first month, a payment of m is made on Loan A, which includes one month of interest. The remaining balance on Loan A is then P_1.
Let j be the monthly effective interest rate of Loan B, assuming there are 12 equal months in a year and 365 days in a year.
Determine which of the following represents j.
- A)
\left[1+\dfrac{1}{12}\left(\dfrac{P_1-P_0+m}{P_0}\right)\right]^{12}-1 - B)
\left[1+12\left(\dfrac{P_1-P_0+m}{P_0}\right)\right]^{1/12}-1 - C)
\left[1+\dfrac{12}{365}\left(\dfrac{P_1-P_0+m}{P_0}\right)\right]^{12}-1 - D)
\left[1+\dfrac{365}{12}\left(\dfrac{P_1-P_0+m}{P_0}\right)\right]^{12/365}-1 - E)
\left[1+\dfrac{12}{365}\left(\dfrac{P_1-P_0+m}{P_0}\right)\right]^{365/12}-1
Answer this question and see the worked solution
Concepts tested
- Nominal Interest Rate
- Loans
- Convertible m-thly
- Nominal Interest Rate Convertible m-thly
- Effective Rate