Financial Mathematics practice questions

Question 1

A car insurance policy pays a claim depending on the event that occurs during a year:

- no claim: probability $0.85$, payout $0$ lei;
- minor damage: probability $0.12$, payout $1000$ lei;
- total loss: probability $0.03$, payout $20000$ lei.

What is the expected value of the payout made by the insurer for this policy?

Accepted Answer

$E(X) = 0.85\cdot 0 + 0.12\cdot 1000 + 0.03\cdot 20000 = 0 + 120 + 600 = 720$ lei.

Check: $0.85+0.12+0.03=1$ (the probabilities cover all cases), and $120+600=720$.

Answer

$600$ lei

Answer

$720$ lei

Answer

$120$ lei

Answer

$21000$ lei

Question 2

A bank deposit of $3000$ lei is placed for one year at a simple annual interest rate of $5\%$. What amount does the interest earned at the end of the year represent?

Accepted Answer

$D = 3000\cdot 0.05 = 150$ lei.

Check: $3000\cdot 5/100 = 150$. (The final amount would be $3150$ lei, but the question asks only for the interest.)

Answer

$150$ lei

Answer

$15$ lei

Answer

$300$ lei

Answer

$3150$ lei

Question 3

A price goes from $\$80$ to $\$100$. The percentage increase is:

Accepted Answer

$\dfrac{100 - 80}{80} \cdot 100\% = \dfrac{20}{80} \cdot 100\% = 25\%$.

Answer

$20\%$

Answer

$22.5\%$

Answer

$25\%$

Answer

$80\%$

Question 4

$15\%$ of $200$ is:

Accepted Answer

$\dfrac{15}{100} \cdot 200 = 30$.

Answer

$15$

Answer

$30$

Answer

$45$

Answer

$300$

Question 5

A deposit of $\$1{,}000$ earns simple interest at $4\%$ per year. After $5$ years, the total interest earned is:

Accepted Answer

$I = 1000 \cdot 0.04 \cdot 5 = 200$.

Answer

$\$40$

Answer

$\$50$

Answer

$\$200$

Answer

$\$1{,}200$

Question 6

A worker invests $\$1{,}000$ at the end of each year into an account paying $5\%$ annual compound interest. The account balance at the end of year $3$ (just after the third deposit) is:

Accepted Answer

$FV = 1000 \cdot \dfrac{1.05^3 - 1}{0.05} = 1000 \cdot \dfrac{0.157625}{0.05} = 1000 \cdot 3.1525 = \$3{,}152.50$.

Answer

$\$3{,}000$

Answer

$\$3{,}075$

Answer

$\$3{,}152.50$

Answer

$\$3{,}310$

Question 7

A deposit of $\$2{,}000$ earns annual compound interest at $5\%$. The balance after $2$ years is:

Accepted Answer

$A = 2000 \cdot 1.05^2 = 2000 \cdot 1.1025 = \$2{,}205$.

Answer

$\$2{,}100$

Answer

$\$2{,}200$

Answer

$\$2{,}205$

Answer

$\$2{,}500$

Question 8

An item priced at $\$80$ is on sale at a $25\%$ discount. The sale price is:

Accepted Answer

Discount $= 20$. Sale price $= 80 - 20 = \$60$.

Answer

$\$55$

Answer

$\$60$

Answer

$\$65$

Answer

$\$75$

Question 9

At $7\%$ annual compound interest, the rule of $72$ estimates that money doubles in approximately:

Accepted Answer

$\dfrac{72}{7} \approx 10.3$ years.

Answer

$7$ years

Answer

$10$ years

Answer

$14$ years

Answer

$72$ years

Question 10

The price of a product before VAT is $\$200$. After applying $19\%$ VAT, the final price is:

Accepted Answer

$200 \cdot 1.19 = \$238$.

Answer

$\$219$

Answer

$\$236$

Answer

$\$238$

Answer

$\$262$

Financial Mathematics

Problems & worked solutions

Problem 1 — Intro to Actuarial Reasoning

Problem 2 — Simple Interest

Problem 3 — Financial Mathematics

Problem 4 — Financial Mathematics

Problem 5 — Financial Mathematics

Problem 6 — Financial Mathematics

Problem 7 — Financial Mathematics

Problem 8 — Financial Mathematics

Problem 9 — Financial Mathematics

Problem 10 — Financial Mathematics

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