NAFA CAFS (core) Practice Exam
Questions and Answers with
Rationales Top Rated A+
1) Financial Mathematics / Discounting
1. If the annual effective interest rate is i=8%i = 8\%i=8%, the present value factor for 3 years is:
A. (1.08)−2(1.08)^{-2}(1.08)−2
B. (1.08)−3(1.08)^{-3}(1.08)−3
C. 1/0.921/0.921/0.92
D. (1.08)3(1.08)^3(1.08)3
Answer: B
Rationale: Present value uses vn=(1+i)−nv^n = (1+i)^{-n}vn=(1+i)−n, so (1.08)−3(1.08)^{-
3}(1.08)−3.
2. A cashflow of 1,000 received at time 4 has present value (at time 0) under i=6%i=6\%i=6%:
A. 1000(1.06)41000(1.06)^41000(1.06)4
B. 1000(1.06)−41000(1.06)^{-4}1000(1.06)−4
C. 1000/1.061000/1.061000/1.06
D. 1000(0.94)41000(0.94)^41000(0.94)4
Answer: B
Rationale: PV is PV=FV(1+i)t=1000(1.06)−4PV = \dfrac{FV}{(1+i)^t} = 1000(1.06)^{-
4}PV=(1+i)tFV=1000(1.06)−4.
3. Under nominal annual rate j(2)=10%j^{(2)} = 10\%j(2)=10% convertible semiannually, the
effective annual rate is:
A. 10%
B. 5%
C. (1+0.10/2)2−1(1+0.10/2)^2 -1(1+0.10/2)2−1
D. 1/(1+0.10/2)2−11/(1+0.10/2)^2 -11/(1+0.10/2)2−1
Answer: C
Rationale: Effective annual i=(1+j/2)2−1i = (1 + j/2)^{2} - 1i=(1+j/2)2−1.
4. If v=11+iv = \frac{1}{1+i}v=1+i1, then iii in terms of vvv is:
A. i=1−vi = 1-vi=1−v
B. i=1v−1i = \frac{1}{v}-1i=v1−1
C. i=v−1i = v-1i=v−1
D. i=11+vi = \frac{1}{1+v}i=1+v1
Answer: B
,Rationale: v=(1+i)−1⇒1+i=1/v⇒i=1/v−1v = (1+i)^{-1} \Rightarrow 1+i = 1/v \Rightarrow
i=1/v - 1v=(1+i)−1⇒1+i=1/v⇒i=1/v−1.
5. If a liability pays 500 at t=1t=1t=1 and 500 at t=2t=2t=2, under i=10%i=10\%i=10%, its PV is:
A. 500(1.1)−1+500(1.1)−2500(1.1)^{-1} + 500(1.1)^{-2}500(1.1)−1+500(1.1)−2
B. 1000(1.1)−21000(1.1)^{-2}1000(1.1)−2
C. 500(1.1)1+500(1.1)2500(1.1)^1 + 500(1.1)^2500(1.1)1+500(1.1)2
D. 1000(1.1)−11000(1.1)^{-1}1000(1.1)−1
Answer: A
Rationale: PV sums each discounted cashflow.
2) Annuities & Loan Equivalence
6. The present value of a 1-year deferred annuity-immediate with payment 1 each year for nnn
years at interest iii is:
A. a¨x\ddot{a}_xa¨x
B. va¨nv\ddot{a}_{n}va¨n
C. a¨n−1\ddot{a}_{n} - 1a¨n−1
D. 1−vni\dfrac{1-v^n}{i}i1−vn without deferral
Answer: B
Rationale: Deferred by 1 year multiplies PV by vvv.
7. The accumulation factor for 5 years at effective rate iii is:
A. (1+i)−5(1+i)^{-5}(1+i)−5
B. 11+i\frac{1}{1+i}1+i1
C. (1+i)5(1+i)^5(1+i)5
D. 1−(1+i)51-(1+i)^51−(1+i)5
Answer: C
Rationale: Accumulation grows by (1+i)t(1+i)^t(1+i)t.
8. For a level-payment loan with constant payment RRR, the loan PV equals:
A. RRR only
B. Ra¨n‾∣iR \ddot{a}_{\overline{n}|i}Ra¨n∣i
C. Ra¨n‾∣i+iRR \ddot{a}_{\overline{n}|i} + iRRa¨n∣i+iR
D. R an‾∣iR \, a_{\overline{n}|i}Ran∣i without timing correction
Answer: B
Rationale: Loan PV is payment amount times PV annuity factor depending on timing.
9. If payments are made at the beginning of each period (annuity-due), the PV factor is:
A. a¨n‾∣i=1−vndv\ddot{a}_{\overline{n}|i} = \frac{1-v^n}{d}va¨n∣i=d1−vnv
B. a¨n‾∣i=(1+i) an‾∣i\ddot{a}_{\overline{n}|i} = (1+i)\, a_{\overline{n}|i}a¨n∣i=(1+i)an∣i
C. a¨n‾∣i=an‾∣i−1\ddot{a}_{\overline{n}|i} = a_{\overline{n}|i} - 1a¨n∣i=an∣i−1
D. a¨n‾∣i=an‾∣i/(1+i)\ddot{a}_{\overline{n}|i} = a_{\overline{n}|i} / (1+i)a¨n∣i=an∣i/(1+i)
, Answer: B
Rationale: Annuity-due PV = annuity-immediate PV × (1+i)(1+i)(1+i).
10. For an ordinary annuity immediate, the PV is:
A. a¨=1−vni(1+i)\ddot{a} = \frac{1-v^n}{i} (1+i)a¨=i1−vn(1+i)
B. a=1−vnia = \frac{1-v^n}{i}a=i1−vn
C. a=1−vnda = \frac{1-v^n}{d}a=d1−vn
D. a=vn/ia = v^n/ia=vn/i
Answer: B
Rationale: Standard ordinary annuity factor: an‾∣i=1−vnia_{\overline{n}|i} = \frac{1-
v^n}{i}an∣i=i1−vn.
3) Bonds, Duration, Convexity (Conceptual + Computation)
11. The clean price of a bond differs from the dirty price because:
A. Clean excludes principal only
B. Clean excludes coupon interest accrued since last payment
C. Clean includes accrued interest
D. Clean equals par value
Answer: B
Rationale: Dirty price = clean price + accrued interest.
12. Macaulay duration approximates the time-weighted PV of cashflows divided by price:
A. True
B. False
C. Only for zero-coupon bonds
D. Only when coupon rate = yield
Answer: A
Rationale: By definition, duration is the weighted average time of cashflows.
13. If yield increases, bond price generally:
A. Increases
B. Decreases
C. Unchanged
D. Becomes infinite
Answer: B
Rationale: Price and yield move inversely.
14. Convexity generally improves duration approximation when:
A. Price changes are large (higher yield moves)
B. Yield changes are zero
C. No interest-rate risk exists
D. Bonds are risk-free only
Questions and Answers with
Rationales Top Rated A+
1) Financial Mathematics / Discounting
1. If the annual effective interest rate is i=8%i = 8\%i=8%, the present value factor for 3 years is:
A. (1.08)−2(1.08)^{-2}(1.08)−2
B. (1.08)−3(1.08)^{-3}(1.08)−3
C. 1/0.921/0.921/0.92
D. (1.08)3(1.08)^3(1.08)3
Answer: B
Rationale: Present value uses vn=(1+i)−nv^n = (1+i)^{-n}vn=(1+i)−n, so (1.08)−3(1.08)^{-
3}(1.08)−3.
2. A cashflow of 1,000 received at time 4 has present value (at time 0) under i=6%i=6\%i=6%:
A. 1000(1.06)41000(1.06)^41000(1.06)4
B. 1000(1.06)−41000(1.06)^{-4}1000(1.06)−4
C. 1000/1.061000/1.061000/1.06
D. 1000(0.94)41000(0.94)^41000(0.94)4
Answer: B
Rationale: PV is PV=FV(1+i)t=1000(1.06)−4PV = \dfrac{FV}{(1+i)^t} = 1000(1.06)^{-
4}PV=(1+i)tFV=1000(1.06)−4.
3. Under nominal annual rate j(2)=10%j^{(2)} = 10\%j(2)=10% convertible semiannually, the
effective annual rate is:
A. 10%
B. 5%
C. (1+0.10/2)2−1(1+0.10/2)^2 -1(1+0.10/2)2−1
D. 1/(1+0.10/2)2−11/(1+0.10/2)^2 -11/(1+0.10/2)2−1
Answer: C
Rationale: Effective annual i=(1+j/2)2−1i = (1 + j/2)^{2} - 1i=(1+j/2)2−1.
4. If v=11+iv = \frac{1}{1+i}v=1+i1, then iii in terms of vvv is:
A. i=1−vi = 1-vi=1−v
B. i=1v−1i = \frac{1}{v}-1i=v1−1
C. i=v−1i = v-1i=v−1
D. i=11+vi = \frac{1}{1+v}i=1+v1
Answer: B
,Rationale: v=(1+i)−1⇒1+i=1/v⇒i=1/v−1v = (1+i)^{-1} \Rightarrow 1+i = 1/v \Rightarrow
i=1/v - 1v=(1+i)−1⇒1+i=1/v⇒i=1/v−1.
5. If a liability pays 500 at t=1t=1t=1 and 500 at t=2t=2t=2, under i=10%i=10\%i=10%, its PV is:
A. 500(1.1)−1+500(1.1)−2500(1.1)^{-1} + 500(1.1)^{-2}500(1.1)−1+500(1.1)−2
B. 1000(1.1)−21000(1.1)^{-2}1000(1.1)−2
C. 500(1.1)1+500(1.1)2500(1.1)^1 + 500(1.1)^2500(1.1)1+500(1.1)2
D. 1000(1.1)−11000(1.1)^{-1}1000(1.1)−1
Answer: A
Rationale: PV sums each discounted cashflow.
2) Annuities & Loan Equivalence
6. The present value of a 1-year deferred annuity-immediate with payment 1 each year for nnn
years at interest iii is:
A. a¨x\ddot{a}_xa¨x
B. va¨nv\ddot{a}_{n}va¨n
C. a¨n−1\ddot{a}_{n} - 1a¨n−1
D. 1−vni\dfrac{1-v^n}{i}i1−vn without deferral
Answer: B
Rationale: Deferred by 1 year multiplies PV by vvv.
7. The accumulation factor for 5 years at effective rate iii is:
A. (1+i)−5(1+i)^{-5}(1+i)−5
B. 11+i\frac{1}{1+i}1+i1
C. (1+i)5(1+i)^5(1+i)5
D. 1−(1+i)51-(1+i)^51−(1+i)5
Answer: C
Rationale: Accumulation grows by (1+i)t(1+i)^t(1+i)t.
8. For a level-payment loan with constant payment RRR, the loan PV equals:
A. RRR only
B. Ra¨n‾∣iR \ddot{a}_{\overline{n}|i}Ra¨n∣i
C. Ra¨n‾∣i+iRR \ddot{a}_{\overline{n}|i} + iRRa¨n∣i+iR
D. R an‾∣iR \, a_{\overline{n}|i}Ran∣i without timing correction
Answer: B
Rationale: Loan PV is payment amount times PV annuity factor depending on timing.
9. If payments are made at the beginning of each period (annuity-due), the PV factor is:
A. a¨n‾∣i=1−vndv\ddot{a}_{\overline{n}|i} = \frac{1-v^n}{d}va¨n∣i=d1−vnv
B. a¨n‾∣i=(1+i) an‾∣i\ddot{a}_{\overline{n}|i} = (1+i)\, a_{\overline{n}|i}a¨n∣i=(1+i)an∣i
C. a¨n‾∣i=an‾∣i−1\ddot{a}_{\overline{n}|i} = a_{\overline{n}|i} - 1a¨n∣i=an∣i−1
D. a¨n‾∣i=an‾∣i/(1+i)\ddot{a}_{\overline{n}|i} = a_{\overline{n}|i} / (1+i)a¨n∣i=an∣i/(1+i)
, Answer: B
Rationale: Annuity-due PV = annuity-immediate PV × (1+i)(1+i)(1+i).
10. For an ordinary annuity immediate, the PV is:
A. a¨=1−vni(1+i)\ddot{a} = \frac{1-v^n}{i} (1+i)a¨=i1−vn(1+i)
B. a=1−vnia = \frac{1-v^n}{i}a=i1−vn
C. a=1−vnda = \frac{1-v^n}{d}a=d1−vn
D. a=vn/ia = v^n/ia=vn/i
Answer: B
Rationale: Standard ordinary annuity factor: an‾∣i=1−vnia_{\overline{n}|i} = \frac{1-
v^n}{i}an∣i=i1−vn.
3) Bonds, Duration, Convexity (Conceptual + Computation)
11. The clean price of a bond differs from the dirty price because:
A. Clean excludes principal only
B. Clean excludes coupon interest accrued since last payment
C. Clean includes accrued interest
D. Clean equals par value
Answer: B
Rationale: Dirty price = clean price + accrued interest.
12. Macaulay duration approximates the time-weighted PV of cashflows divided by price:
A. True
B. False
C. Only for zero-coupon bonds
D. Only when coupon rate = yield
Answer: A
Rationale: By definition, duration is the weighted average time of cashflows.
13. If yield increases, bond price generally:
A. Increases
B. Decreases
C. Unchanged
D. Becomes infinite
Answer: B
Rationale: Price and yield move inversely.
14. Convexity generally improves duration approximation when:
A. Price changes are large (higher yield moves)
B. Yield changes are zero
C. No interest-rate risk exists
D. Bonds are risk-free only
