Question 1

What is the future value of $12 000 on deposit for four years at 7.00% per annum simple interest?

Accepted Answer

The future value using simple interest is calculated as $FV = P(1 + rt)$, where $P$ is the principal amount ($12,000), $r$ is the annual interest rate (7% or 0.07), and $t$ is the time in years (4). Thus, $FV = 12000(1 + 0.07 \times 4) = 12000(1 + 0.28) = 12000 \times 1.28 = $15,360.00$.

Question 2

If a company sells (discounts)a bank bill with a face value of $100 000,a term to maturity of 90 days,and a yield of 7.23% per annum,how much will the company raise on the issue? (Ignore transaction fees.)

Accepted Answer

To calculate the amount raised by the company, we need to use the formula:
Amount raised = Face value x (1 - discount rate x time to maturity)
where,
Face value = $100,000
Discount rate = yield rate / 365 = 0.0723 / 365 = 0.000198
Time to maturity = 90 / 365 = 0.2466 years

Plugging in these values, we get:
Amount raised = $100,000 x (1 - 0.000198 x 0.2466) = $98,248.49

So, the company will raise $98,248.49 on the issue. Therefore, the best choice is B.

Question 3

If you borrow $100 000 for 90 days with simple interest of 6.2% per annum,what is the total amount of interest paid on the loan?

Accepted Answer

Interest = (P * R * T) / 100= (100000 * 6.2 * 90) / 100 * 365= 1528.77

Question 4

A 90-day promissory note with a face value of $500 000 is issued at a yield of 7.789% per annum.Calculate its price.

Accepted Answer

The price of a promissory note can be calculated using the formula: Price = Face Value / (1 + (Yield * (Days to Maturity/365))). Plugging in the given values: Price = $500,000 / (1 + (0.07789 * (90/365))) = $490,578.08.

Question 5

What is the present value of $1 million payable in 90 days at 8.00% per annum simple interest?

Accepted Answer

The present value (PV) can be calculated using the formula PV = FV / (1 + rt), where FV is the future value ($1 million), r is the annual interest rate (8.00% or 0.08), and t is the time in years (90 days / 365 days = 0.2466 years). Plugging in the values: PV = $1,000,000 / (1 + 0.08 * 0.2466) = $1,000,000 / 1.01973 ≈ $980,655.56.

Question 6

If you receive $100 000 back as principal and interest for an investment of $92 368 that you made six months earlier,what simple rate of interest has been earned on your investment?

Accepted Answer

The answer of If you receive $100 000 back as...

Question 7

If you invest $7500 for a year at 7.4% per annum simple interest,what is the value of your investment at the end of the year?

Accepted Answer

To calculate the value of the investment at the end of the year, we use the formula:
Simple Interest = (Principal x Rate x Time)/100
Here, the principal (P) = $7500, the rate (R) = 7.4% and the time (T) = 1 year.
Plugging these values into the formula, we get:
Simple Interest = (7500 x 7.4 x 1)/100 = $555
Therefore, the value of the investment at the end of the year is:
7500 + Simple Interest = $7500 + $555 = $8055
Hence, the answer is C.

Question 8

When a company sells a commercial bill,this means the company:

Accepted Answer

Selling a commercial bill means that the company is issuing a commercial bill, which is a short-term debt instrument that indicates a promise to pay a specific sum of money on a specific date in the future.

Question 9

The term 'simple',with regard to interest,refers to the fact that:

Accepted Answer

The term 'simple' refers to the fact that interest is calculated on the initial principal only and not on any interest earned over time. This is in contrast to compound interest, where interest is calculated on both the original principal and any accumulated interest. Therefore, option D is the correct answer. Options A, B, and C are incorrect as they do not relate to the term 'simple' specifically in the context of interest calculations.

Question 10

The market convention to use a 360-day year in the financial markets applies in:

Accepted Answer

The 360-day year convention is commonly used in the United States and euromarkets for calculating interest on loans, bonds, and other financial instruments. This simplifies the interest calculation process by standardizing the number of days in a month to 30.

Question 11

When a company discounts a commercial bill,this means the company:

Accepted Answer

When a company discounts a commercial bill, it means that they are receiving cash immediately in exchange for the bill before the maturity date. This is a form of borrowing as they are obtaining funds through this transaction.

Question 12

If you invest $1200 for two years at 6.9% per annum simple interest,what is the value of your investment at the end of the two years?

Accepted Answer

Using the formula for simple interest: 
I = P * r * t 
where I is the interest earned, P is the principal or initial investment, r is the annual interest rate, and t is the time in years.
We have: 
I = 1200 * 0.069 * 2 = $165.60 
The value of the investment at the end of two years will be the sum of the principal and the interest earned: 
Value = Principal + Interest = $1200 + $165.60 = $1365.60. 
Therefore, the best choice is B.

Question 13

If you receive $100 000 back as principal and interest at the end of the year for an initial investment of $93 456 at the start of the year,what interest has been earned on your investment?

Accepted Answer

To find out the interest earned, we need to calculate the difference between the final amount received and the initial investment.

Final amount = Principal + Interest = $100,000
Initial investment = $93,456

Interest earned = Final amount - Initial investment = $100,000 - $93,456 = $6,544

Now, we need to calculate the percentage of interest earned on the initial investment:

Interest percentage = (Interest earned / Initial investment) x 100
= ($6,544 / $93,456) x 100
= 7.00%

Therefore, the answer is C, 7.00%.

Question 14

If a company sells (discounts)a bank bill with a face value of $500 000,a term to maturity of 120 days,and a yield of 8.45% per annum,how much will the company raise on the issue? (Ignore transaction fees.)

Accepted Answer

The formula to calculate the amount raised on a discounted bank bill is as follows:

Amount raised = Face value * (1 - Discount rate * Time to maturity/360)

Plugging in the given values, we get:

Amount raised = $500,000 * (1 - 0.0845*120/360) = $486,485.05

Therefore, the best choice is C, which is the closest option to the calculated amount.

Question 15

If you invest $1600 for a year at 6.8% per annum simple interest,how much interest will you earn?

Accepted Answer

To find out the interest earned, we can use the formula:
Interest = (Principal x Rate x Time)/100
Here, Principal = $1600, Rate = 6.8%, and Time = 1 year
Substituting the values, we get:
Interest = (1600 x 6.8 x 1)/100 = $108.00
Hence, the correct answer is option B, $108.00.

Question 16

If you receive $10 000 back as principal and interest at the end of two years for an initial investment of $9127 at the start of the term,what is the yield on your investment?

Accepted Answer

We can use the formula for compound interest to solve this problem:

A = P(1+r)^n

Where:
A = final amount
P = initial investment
r = interest rate as a decimal
n = number of compounding periods

We know that A = $10,000, P = $9,127, and n = 2 years. We can solve for r:

$10,000 = $9,127(1+r)^2
(1+r)^2 = $10,000/$9,127
(1+r)^2 = 1.0957
1+r = √1.0957
1+r = 1.0478
r = 0.0478 or 4.78%

Therefore, the yield on the investment is 4.78% per annum, which corresponds to choice B.

Question 17

If you invest $13 500 for 18 months at 6.9% per annum simple interest,what is the value of your investment at the end of the 18 months?

Accepted Answer

Using the formula for simple interest: 
I = Prt 
where I is the interest earned, P is the principal (initial investment), r is the interest rate per annum as a decimal, and t is the time period in years.

In this case, 
P = $13 500 
r = 0.069 (since 6.9% is the same as 0.069 as a decimal) 
t = 1.5 years (since 18 months is 1.5 years)

I = (13 500)(0.069)(1.5) 
I = $1407.75

To find the value of the investment at the end of the 18 months, we add the interest earned to the initial investment:

Value = P + I 
Value = $13 500 + $1407.75 
Value = $14 907.75

The closest option to this value is choice B, $14 897.25.

Question 18

When a company discounts a commercial bill to obtain funds,this means the company:

Accepted Answer

When a company discounts a commercial bill, it essentially sells the bill (usually to a bank) before it matures at a price lower than its face value to obtain funds immediately. This does not involve issuing, lending, buying, or investing in commercial bills directly but rather selling a bill the company already holds.

Question 19

If the current yield on 180-day Treasury notes is 6.42% per annum,what price per $100 of face value would an investor pay to purchase them?

Accepted Answer

The formula used to calculate bond price is: 
Bond price = Face value / (1 + yield/2)^(n/6)

Here, face value = $100, yield = 6.42%, n = 180 days.

Substituting these values in the formula, we get:
Bond price = 100 / (1 + 0.0642/2)^(180/6)
Bond price = $96.94 (approx.)

Therefore, the correct answer is C.

Question 20

If you invest _______ to earn simple interest of 6.8% per year,you will receive $12 375 at the end of two years.

Accepted Answer

The answer of If you invest _______ to earn simple...

Quiz 8: Mathematics of Finance: An Introduction to Basic Concepts and Calculations