Free SOA Exam FM Time Value of Money Practice Questions (2026)

Sample Questions

Question 1 Easy

Calculate the present value of $50,000 due in 12 years at an effective annual interest rate of 3%.

Solution

C is correct.

The present value is:

P V = F V \cdot v^{n} = \frac{F V}{( 1 + i ) ^{n}} = \frac{50 , 000}{( 1.03 ) ^{12}}

Compute

(1.03)^{12}

by repeated squaring:

(1.03)^{2} = 1.0609

(1.03)^{4} = (1.0609)^{2} = 1.12550881

(1.03)^{8} = (1.12550881)^{2} = 1.26677008

(1.03)^{12} = (1.03)^{8} \times (1.03)^{4} = 1.26677008 \times 1.12550881 = 1.42576089

P V = \frac{50 , 000}{1.42576089} = 35, 069

The present value is $35,069.

Question 2 Medium

A nominal interest rate of 6% compounded semiannually is given. Determine the equivalent force of interest

δ

Solution

A is correct.

Step 1: Find the effective annual interest rate.

1 + i = (1 + \frac{0.06}{2})^{2} = (1.03)^{2} = 1.0609

Step 2: Find the force of interest.

δ = ln (1 + i) = ln (1.0609)

Alternatively:

δ = 2 ln (1.03) = 2 \times 0.029559 = 0.059118

.

So

δ \approx 0.05912

Question 3 Hard

Given

i^{(4)} = 10%

, calculate

d^{(6)}

Solution

E is correct.

Convert

i^{(4)}

to the force of interest

δ

δ = 4 ln (1 + \frac{i ^{(4)}}{4}) = 4 ln (1.025) = 4 \times 0.024693 = 0.098771

Convert

δ

d^{(6)}

d^{(6)} = 6 (1 - e^{- δ /6}) = 6 (1 - e^{- 0.016462})

e^{- 0.016462} = 0.98367

d^{(6)} = 6 \times 0.01633 = 0.09796 \approx 9.80%

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Free SOA Exam FM (Financial Mathematics) Time Value of Money Practice Questions

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