Free SOA Exam FM Loans Practice Questions (2026)

Sample Questions

Question 1 Easy

Which of the following best describes the term of a loan?

Solution

E is correct.

The term of a loan is the length of time from when the loan is originated to when the final payment is made and the loan is fully retired. For example, a 30-year mortgage has a term of 30 years.

Question 2 Medium

A $28,000 loan at 6% effective annual interest is repaid with 8 level annual payments. Determine the total interest paid in the first 3 payments.

Solution

C is correct.

Annual payment:

a_{8 ∣0.06} = \frac{1 - ( 1.06 ) ^{- 8}}{0.06} = 6.20979

P = \frac{28 , 000}{6.20979} = 4, 509.17

Compute the interest portion of each of the first three payments (interest = rate

\times

outstanding balance):

I_{1} = 0.06 \times 28, 000 = 1, 680.00

B_{1} = 28, 000 - (4, 509.17 - 1, 680.00) = 25, 170.83

I_{2} = 0.06 \times 25, 170.83 = 1, 510.25

B_{2} = 25, 170.83 - (4, 509.17 - 1, 510.25) = 22, 171.91

I_{3} = 0.06 \times 22, 171.91 = 1, 330.31

Total interest in the first three payments:

1, 680.00 + 1, 510.25 + 1, 330.31 = 4, 520.56 \approx 4, 521

Question 3 Hard

A loan of $80,000 is repaid with level annual payments at the end of each year for 25 years at an annual effective interest rate of 6%. Determine the interest portion of the 10th payment.

Solution

D is correct.

The annual payment is:

P M T = \frac{80 , 000}{a _{25 ∣}} at i = 0.06

v = 1/1.06

v^{25} = 0.232999

a_{25 ∣} = \frac{1 - 0.232999}{0.06} = \frac{0.767001}{0.06} = 12.783356

P M T = \frac{80 , 000}{12.783356} = 6, 258.14

The interest portion of the 10th payment equals

i \times O B_{9}

, where

O B_{9}

is the outstanding balance after 9 payments:

O B_{9} = P M T \cdot a_{16 ∣}

v^{16} = 0.393646

a_{16 ∣} = \frac{1 - 0.393646}{0.06} = \frac{0.606354}{0.06} = 10.105895

O B_{9} = 6, 258.14 \times 10.105895 = 63, 244.08

I_{10} = 0.06 \times 63, 244.08 = 3, 794.64 \approx 3, 795

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