Financial Math



Taking a Securities Certification Exam?   Or thinking of a career as a securities salesperson?  You will have to know some math!   Practice your financial math here.


1. A newly wedded couple decided to invest in a 10% municipal bond that is aimed to support a local development project. Their plan was to buy the bond at $2,000 but could only purchase it at $2,050. A year later, the couple decides to make a profit and sell off the bond to when the market value has dropped to $2,000.

What is the expected return?

a. 8.98%
b. 10%
c. 7.6%
d. 2.4%

2. A woman buys a 12% bond at $1,000. A year later the market value of the bond drops to $950. Calculate the woman’s return if she sold the bond after a year.

a. 7%
b. $50
c. 12%
d. 17%

3. Below is the margin account of a customer:

· Long 400 shares PDQ @ 60
· Short 250 shares FBN @ 35
· Credit balance = $17,000
· Debit balance = $12,000

What is the customer’s combined equity?

a. $15,000
b. $8,250
c. $24,000
d. $20,250

4. A banker invested $1,000 in a mutual fund. The first year the mutual fund gained 30%, and lost 15% in the second year.  Calculate the value of the mutual fund at the end of two years.

a. $1,005
b. $1,105
c. $1,225
d. $1,150

5. A woman bought 150 shares of a company at $40 a share. After one year, she sold all the shares at $50 a share. Before selling the shares, she received dividends of $2 per share. Calculate her Holding Period Return.

a. 30%
b. 20%
c. 27%
d. 35%

6. David, who lives in Georgia, invested in a U.S government Treasury Bond that offered a yearly interest of 10%. His State of Georgia tax rate is 8%, while his federal income tax rate is 25%. Calculate his after-tax yield.  

a. 7.2%
b. 5.5%
c. 7.5%
d. 6.5%

7. A certain large fast food company’s stock is being sold at $60 and it pays no dividend. A recent dependable analysis report indicates that the company’s stock is going to earn $2.50 per share, and that the P/E ratio is 20. Based on the information given, which of the following would be correct?

a. Not enough information provided to evaluate the stock
b. The stock is selling proportionally with its current market price
c. The stock is undervalued
d. The stock is overvalued

8. A widow has just been informed that her husband bought a $1,500 par value bond that offers a 10% coupon. The bond is redeemable at par in 10 years and is presently sold at $100. What is the amount of interest that is payable yearly?

a. $125
b. $100
c. $150
d. $15

9. Use the following information about a customer’s margin account to answer the question.

· ZYX stock – 150 shares. CMV $50/share
· QWT stock – 200 shares. CMV $40/share
· ACB stock – 300 shares. CMV $30/ share
· Debit balance — $10,500

From the information above, this account:

a. is under margined
b. has excess equity
c. is restricted
d. is in a position for a maintenance call


Answer Key


1. C
The question is trying to confuse with irrelevant details. The fact that the couple wanted to buy the bond for $2,000 does not matter. What matters is they bought it at $2,050. The next year when they decide to sell, the value of the bond has depreciated from $2,050 to $2,000. The return from selling the bond would reflect the interest earned minus the depreciation caused by the fall in market value. The bond earned 10% but lost almost 2.4%, which means it delivers a return of 7.6%.

($2050-$2000 = $50)/$2050 x 100 = 2.4%. (10% + (-2.4%) = 7.6%

2. A
The return on investment on a bond depends on the interest rate, which is 12% in the case. The total return must however reflect any addition or subtraction caused by an appreciation or depreciation of the bond’s value. In this example, the bond depreciated from $1,000 to $950. The percentage lost is ($1,000-$950 = $50)/ $1,000 x 100 = 5%. Since the bond pays 12% interest, total return on this investment is 12%-5%= 7%

3. D
Since the complete account information is provided, we can easily calculate equity using the formulas for long and short account

Long account: Current market value – debit
Short account: Credit – Market value short = equity
Long account = (400 x 60)$24,000 – $12,000 = $12,000
Short Account = $17,000 – $8,750(250×35) = $8,250

Total equity in account = $12,000+$8,250 = $20,250

4. B
The mutual fund earned 30% on $1,000 in the first year, which is $300. That means the mutual fund was worth $1,300 at the end of the first year. In the second year, it now lost 15% on $1,300, which is $195. The value of the mutual fund at the end of 2 years is $1,300-$195= $1,105

5. A
To calculate HPR or Holding Period Return, we use the formula: Total Return divided by the Total Cost of investment. Total return is calculated by adding all dividends, income, appreciation and deducting depreciation and margin interest. In this case, the total return is $7,500 (proceeds) + $300 (dividend) – $6,000 (Cost) = $1800. So, HPR is $1800/$6000 x 100 = 30%

6. C
Interests and earnings accrued from U.S government bonds are not subject to state or local taxes. They are not, however, exempt from federal taxes. This makes it important for investors planning to invest in a taxable or non-taxable investment, to first calculate the tax-exempt yield. A tax-exempt yield would only be considered attractive if its yield is above 4.9%

The formula to compute tax-exempt yield is to take the taxable-equivalent Yield and multiply it by (1-Marginal tax rate) which equals the tax-exempt yield.

In this case, 0.1 x (1-0.25)= 0.075 or 7.5%

7. D
The current market price of the stock is $50, so the stock is presently overvalued. The current market price is calculated using = earnings times P/E ratio. In this case, $2.50 x 20 = $50

8. C
The question contains some information that is not relevant in calculating annual interest on income. The par bond is worth $1,500 and its offers a 10% coupon. This simply means that the annual interest is 10% of $1,500, which is $150. The maturity date or present selling price does not affect the calculation of yearly interest.

9. B
This is a long margin account. Formula for calculating equity on this account is: CMV-DR=EQ

CMV = $7,500+$8,000+$9,000 = (24,500 CMV – 10,500 DR = 14,000 EQ).
To calculate the EQ or equity required, we multiply CMV by 50%
50% of $24,500 is $12,250. So this account has excess equity.


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