Training Financial Mathematics Placement Test Practice — Financial Math
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Placement Test Practice — Financial Math

23 min Financial Mathematics

Placement Test Practice — Financial Math

Practice Test — 20 Questions

1. Simple interest: $\$4{,}000$ at $3\%$ for 5 years.
2. Compound amount: $\$2{,}000$ at $5\%$ annually, 8 years.
3. EAR for $6\%$ compounded quarterly?
4. PV of $\$30{,}000$ in 12 years at $4\%$.
5. FV of $\$150$/month for 20 years at $6\%$ monthly.
6. Monthly payment: $\$180{,}000$ mortgage, $5\%$, 30 years.
7. Total interest on the mortgage above.
8. PV of perpetuity: $\$500$/year at $4\%$.
9. How long to triple at $8\%$ compounded annually?
10. Monthly savings to reach $\$1{,}000{,}000$ in 40 years at $7\%$ monthly.
11. PV of $\$800$/month for 5 years at $6\%$ monthly.
12. What is an amortization schedule?
13. Sinking fund payment for $\$100{,}000$ in 15 years at $5\%$ annually.
14. Which has higher EAR: $10\%$ semi-annual or $9.8\%$ monthly?
15. Continuous PV: $\$50{,}000$ in 10 years at $4\%$.
16. Interest portion of first mortgage payment: $\$250{,}000$ at $4.5\%$.
17. Annuity due vs. ordinary annuity: which has higher FV?
18. Find rate: $\$1{,}000$ grows to $\$1{,}500$ in 6 years (annually).
19. Net Present Value: invest $\$10{,}000$ now, receive $\$3{,}000$/year for 4 years, $r = 8\%$.
20. Rule of 72: doubling time at $4\%$?
Show Answer Key

1. $I = 4000(0.03)(5) = \$600$

2. $2000(1.05)^8 \approx \$2{,}954.91$

3. $(1.015)^4-1 \approx 6.14\%$

4. $30000/(1.04)^{12} \approx \$18{,}726.15$

5. $150 \cdot \frac{(1.005)^{240}-1}{0.005} \approx \$69{,}299$

6. $R \approx \$966.28$

7. $360(966.28)-180000 \approx \$167{,}861$

8. $500/0.04 = \$12{,}500$

9. $\ln 3/\ln 1.08 \approx 14.27$ years

10. $R \approx \$381$

11. $PV \approx \$41{,}398.40$

12. Table showing payment-by-payment interest, principal, and balance

13. $R = \frac{100000(0.05)}{(1.05)^{15}-1} \approx \$4{,}634.23$

14. $10\%$ semi: $10.25\%$; $9.8\%$ monthly: $(1+0.098/12)^{12}-1 \approx 10.25\%$; nearly equal

15. $50000 e^{-0.4} \approx \$33{,}516.00$

16. $250000(0.045/12) = \$937.50$

17. Annuity due (starts earlier)

18. $r = (1.5)^{1/6}-1 \approx 6.99\%$

19. $NPV = -10000 + 3000 \cdot \frac{1-1.08^{-4}}{0.08} \approx -10000+9936 = -\$64$ (marginal)

20. $72/4 = 18$ years

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