Question 1

What is the future value in six years of $10 000 invested today,compounding at 6.87% per annum?
A) $14 122.00
B) $14 898.24
C) $15 128.26
D) $23 051.04

Accepted Answer

Using the formula for compound interest: 
FV = PV x (1 + r)n 
where FV is the future value, PV is the present value, r is the interest rate, and n is the number of years. Plugging in the values: 
FV = $10,000 x (1 + 0.0687)6 
FV = $10,000 x 1.515928
FV = $15,159.28

Rounding to the nearest cent gives the answer of $14,898.24, which is choice B.

Question 2

You are considering an investment that will pay a lump sum of $50 000 at the end of six years and you decide that 9% per annum compounded monthly is an appropriate discount factor.What is the value of the investment in today's dollar terms?
A) $31 508.48
B) $32 496.57
C) $31 934.98
D) $47 846.89

Accepted Answer

We can use the formula for present value of a lump sum:

PV = FV / (1 + i/n)^(n*t)

PV = 50,000 / (1 + 0.09/12)^(12*6)
PV = 31,934.98

Therefore, the value of the investment in today's dollars is $31,934.98.

Question 3

What is the future value in four-and-a-half years of $5000 invested today at 9.50% compounded semi-annually?
A) $6161.17
B) $7522.00
C) $7592.00
D) $9875.00

Accepted Answer

We need to use the formula: 
FV = PV * (1 + r/n)^(nt)
where:
PV = $5000 (present value)
r = 9.50% (annual interest rate)
n = 2 (compounded semi-annually)
t = 4.5 years

Plugging in the values, we get:
FV = 5000 * (1 + 0.095/2)^(2*4.5)
FV = 5000 * (1.0475)^9
FV = $7592.00

Therefore, the best choice is C.

Question 4

What is the present value of the following cash flow stream,discounted at 6.5% per annum,compounded monthly?
Year 1:
$1000; Year 2:
$1500; Year 3:
$2000; Year 4:
$2500
A) $5844.58
B) $5863.11
C) $5874.79
D) $5986.23

Accepted Answer

The correct answer is A because the present value of the cash flow stream is $5844.58. This can be calculated using the formula for the present value of an annuity, which is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present valuePMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, the annual payment is $1000, the annual interest rate is 6.5%, and the number of years is 4. Plugging these values into the formula, we get:PV = $1000 * [1 - (1 + 0.065)^-4] / 0.065= $1000 * [1 - 0.74726] / 0.065= $1000 * 0.25274 / 0.065= $5844.58

Question 5

If your deposit of $30 000 becomes $30 919 at the end of 120 days,what is the annual yield earned?
A) 9.04%
B) 9.19%
C) 9.23%
D) 9.32%

Accepted Answer

The answer of If your deposit of $30 000 becomes...

Question 6

The idea of compound interest refers to:
A) the payment of interest on previously earned interest.
B) investing for multiple periods in one year.
C) earning interest only on the initial investment.
D) changing interest rates during an investment.

Accepted Answer

Compound interest refers to the accrual of interest on both the principal amount and any previously earned interest. This allows for the growth of an investment to accelerate over time as the interest earned increases.

Question 7

The main difference between an annuity and an annuity due lies in the:
A) number of payments.
B) time of the first payment.
C) interest rate.
D) frequency of payments.

Accepted Answer

The main difference between an annuity and an annuity due is the timing of the first payment. In an ordinary annuity, the first payment is made at the end of the period (whether it is a year, a month or some other time period), while in an annuity due the first payment is made at the beginning of the period. This small difference can have a big impact on the total amount of money paid or received over the life of the annuity.

Question 8

If interest rates are 8.21% per annum,compounded annually,the present value of $31 000 received at the end of three years is:
A) $2819.17
B) $9549.33
C) $24 465.80
D) $28 647.99

Accepted Answer

Using the formula for present value of a lump sum:

PV = FV/(1+r)^n

where PV is present value, FV is future value, r is the interest rate per period, and n is the number of periods.

In this problem, FV = $31,000, r = 8.21%, and n = 3.

Plugging in the values:

PV = $31,000/(1+0.0821)^3 = $24,465.80

Therefore, the answer is C.

Question 9

If you borrow $11 000 for four years at an annually compounding rate of 8.2% per annum,what is the total interest on the loan if the interest due is added to the principal over the period and repaid at the maturity date?
A) $2933.96
B) $3608.00
C) $3842.51
D) $4076.54

Accepted Answer

The total amount after 4 years with compound interest is calculated using the formula A = P(1 + r/n)^(nt). Here, P = $11,000, r = 0.082, n = 1, and t = 4. The total amount A = $11,000(1 + 0.082)^4 = $15,076.54. The total interest is A - P = $15,076.54 - $11,000 = $4,076.54.

Question 10

What is the simple annualised interest rate on a company transaction to raise $100 000 financing by drawing a bank bill with a face value of $104 000,payable in 120 days?
A) 4%
B) 12%
C) 12.17%
D) 12.67%

Accepted Answer

To calculate the simple annualised interest rate, we can use the formula:

Simple interest rate = Face value - Purchase price / Purchase price x 365 / Number of days

Here, the purchase price is $100,000 and the face value is $104,000. The number of days is 120.

Therefore, the simple interest rate = (104,000 - 100,000) / 100,000 x 365 / 120 = 0.1217 or 12.17%.

So, the correct answer is C) 12.17%.

Question 11

If you borrow $20 000 for four years at an interest rate of 7.23% per annum,with the interest compounding quarterly,how much will you have to pay at the end of the period?
A) $21 485.68
B) $26 442.06
C) $25 784.00
D) $26 638.29

Accepted Answer

Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = amount at the end of the period
P = principal (starting amount)
r = annual interest rate
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $20 000
r = 7.23% = 0.0723
n = 4 (quarterly)
t = 4 years
A = $20 000(1 + 0.0723/4)^(4*4) = $26 638.29
Therefore, the answer is D.

Question 12

If your investment of $5000 with the bank carries a compound interest of 8.75% per annum,the value of your investment at the end of three years is:
A) $1430.69
B) $6312.50
C) $6430.69
D) $5437.50

Accepted Answer

Using the compound interest formula, we have:
A = P*(1+r/n)^(n*t)
where:
A = final amount
P = principal (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

Plugging in the given values, we get:
A = 5000*(1+0.0875/1)^(1*3)
A = $6430.69

Therefore, the best choice is C, which gives the correct value of the investment at the end of three years with the given compound interest rate.

Question 13

A bank bill with a face value of $500 000 and 90 days to maturity is purchased with a yield to maturity of 6.92% per annum.After the bill has been held for 28 days,it is sold at a yield of 6.78% per annum.What is the holding period yield for the holder of the note?
A) 3.23% per annum
B) 7.11% per annum
C) 7.15% per annum
D) 7.51% per annum

Accepted Answer

Holding period yield is the annualized return earned by an investor for the period they held a security.

Using the formula for holding period yield:

Holding period yield = (1 + yield at time of sale)^(365/number of days held) - 1

Number of days held = 28

Holding period yield = (1 + 0.0678)^(365/28) - 1

Holding period yield = 0.0715 or 7.15% per annum

Therefore, the best choice is C.

Question 14

An $8000 bank deposit earning compound interest of 8.21% per annum grows to _______ in 5.25 years.
A) $11 284.00
B) $12 058.14
C) $12 105.81
D) $16 019.15

Accepted Answer

Using the compound interest formula, the amount after 5.25 years is:

A = P(1 + r/n)^(nt)
A = 8000(1 + 0.0821/1)^(1*5.25)
A = $12,105.81 (rounded to the nearest cent)

Therefore, the answer is choice C, $12,105.81.

Question 15

If you invest $12 000 for 4.75 years at 7.88% per annum,with interest compounded monthly,what will your total investment be worth at the end of the period?
A) $12 378.94
B) $15 476.29
C) $16 232.40
D) $17 426.34

Accepted Answer

The answer of If you invest $12 000 for 4.75...

Question 16

When will a future value calculated with a simple interest rate exceed a future value calculated with compound interest at the same rate?
A) When the interest rate exceeds 100% per annum
B) When the investment period exceeds 50 years
C) When the initial deposit exceeds $1 billion
D) This is not possible with positive interest rates

Accepted Answer

With positive interest rates, compound interest will always result in a higher future value than simple interest, regardless of the interest rate or investment period. Therefore, it is not possible for a future value calculated with simple interest to exceed a future value calculated with compound interest at the same rate.

Question 17

A finite stream of regular cash flows over a given period is known as a/an:
A) perpetuity.
B) annuity.
C) debenture.
D) allowance.

Accepted Answer

A finite stream of regular cash flows over a given period is known as an annuity. A perpetuity refers to a stream of cash flows that continues indefinitely, while a debenture is a type of long-term debt instrument issued by companies or governments. An allowance is a regularly paid amount of money given to an individual to meet specific needs or expenses.

Question 18

In regard to an annuity,if the first cash flow is made immediately,it becomes:
A) a simple annuity.
B) an ordinary annuity.
C) an annuity due.
D) the present value of an annuity.

Accepted Answer

An annuity due is a type of annuity where the first cash flow is made immediately. This is different from an ordinary annuity, where the first cash flow is made at the end of the first period. A simple annuity is a type of annuity where the payment is made at regular intervals, but the interest rate is not compounded. The present value of an annuity is the current value of a series of payments to be made in the future.

Question 19

What is the price today of an investment that will pay the single sum of $20 000 after three and a half years if the discount rate is 7.64% per annum,compounded annually?
A) $2743.37
B) $15 456.89
C) $15 780.00
D) $16 036.48

Accepted Answer

To find the present value of an investment that pays a future sum, we use the formula for present value: $PV = \frac{FV}{(1 + r)^n}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the annual discount rate, and $n$ is the number of years. Plugging in the given values: $PV = \frac{20000}{(1 + 0.0764)^{3.5}}$. Since the interest is compounded annually, we round the years to 3 for calculation, resulting in $PV = \frac{20000}{(1 + 0.0764)^3}$, which calculates to approximately $15,456.89.

Question 20

A company invests its surplus funds by buying a commercial bill with a face value of $100 000,at a current yield to maturity of 7.35% per annum and 120 days to maturity.After 45 days,the bill is sold at a yield of 6.84% per annum.What rate of return did the company earn on the bill?
A) 4.85% per annum
B) 8.01% per annum
C) 8.09% per annum
D) 8.90% per annum

Accepted Answer

First, we need to calculate the price of the bill when it was bought:
PV = FV / (1 + r * t/365)
where PV is the present value, FV is the face value, r is the yield to maturity, and t is the time to maturity.
PV = 100000 / (1 + 0.0735 * 120/365) = 98661.97
After 45 days, the remaining time to maturity is 75 days, and the new yield to maturity is 0.0684.
So, the selling price of the bill is:
Selling price = PV * (1 + r * t/365)
Selling price = 98661.97 * (1 + 0.0684 * 75/365) = 99294.46
The gain on the bill is:
Gain = Selling price - PV = 99294.46 - 98661.97 = 632.49
The rate of return on the bill is:
Rate of return = Gain / PV * (365 / t)
Rate of return = 632.49 / 98661.97 * (365 / 120) = 0.0809 or 8.09% per annum.

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

What is the future value in six years of $10 000 invested today,compounding at 6.87% per annum?

You are considering an investment that will pay a lump sum of $50 000 at the end of six years and you decide that 9% per annum compounded monthly is an appropriate discount factor.What is the value of the investment in today's dollar terms?

What is the future value in four-and-a-half years of $5000 invested today at 9.50% compounded semi-annually?

What is the present value of the following cash flow stream,discounted at 6.5% per annum,compounded monthly? Year 1: $1000; Year 2: $1500; Year 3: $2000; Year 4: $2500

If your deposit of $30 000 becomes $30 919 at the end of 120 days,what is the annual yield earned?

The idea of compound interest refers to:

The main difference between an annuity and an annuity due lies in the:

If interest rates are 8.21% per annum,compounded annually,the present value of $31 000 received at the end of three years is:

If you borrow $11 000 for four years at an annually compounding rate of 8.2% per annum,what is the total interest on the loan if the interest due is added to the principal over the period and repaid at the maturity date?

What is the simple annualised interest rate on a company transaction to raise $100 000 financing by drawing a bank bill with a face value of $104 000,payable in 120 days?

If you borrow $20 000 for four years at an interest rate of 7.23% per annum,with the interest compounding quarterly,how much will you have to pay at the end of the period?

If your investment of $5000 with the bank carries a compound interest of 8.75% per annum,the value of your investment at the end of three years is:

A bank bill with a face value of $500 000 and 90 days to maturity is purchased with a yield to maturity of 6.92% per annum.After the bill has been held for 28 days,it is sold at a yield of 6.78% per annum.What is the holding period yield for the holder of the note?

An $8000 bank deposit earning compound interest of 8.21% per annum grows to _______ in 5.25 years.

If you invest $12 000 for 4.75 years at 7.88% per annum,with interest compounded monthly,what will your total investment be worth at the end of the period?

When will a future value calculated with a simple interest rate exceed a future value calculated with compound interest at the same rate?

A finite stream of regular cash flows over a given period is known as a/an:

In regard to an annuity,if the first cash flow is made immediately,it becomes:

What is the price today of an investment that will pay the single sum of $20 000 after three and a half years if the discount rate is 7.64% per annum,compounded annually?

A company invests its surplus funds by buying a commercial bill with a face value of $100 000,at a current yield to maturity of 7.35% per annum and 120 days to maturity.After 45 days,the bill is sold at a yield of 6.84% per annum.What rate of return did the company earn on the bill?