Question 1

During 2005 the price of a good increased by 8%. In the sales on January 1st 2006, all items are reduced by 25%. If the sale price of the good is $688.50, find the original price at the beginning of 2005.
A)$935
B)$850
C)$558
D)$2,395
E)$925

Accepted Answer

B

Question 2

Determine the monthly repayments needed to repay a $125,000 loan which is paid back over 20 years when the interest rate is 7% compounded annually. Round your answer to two decimal places.
A)$1,078.39
B)$1,172.24
C)$893.86
D)$983.26
E)$971.79

Accepted Answer

D

Question 3

A principal of $70,000 is invested at 6% interest for four years. Find the difference in the future value if the interest is compounded quarterly compared to continuous compounding. Round your answer to two decimal places.
A)$158.45
B)$614.05
C)$256.65
D)$620.43
E)$469.93

Accepted Answer

The future value of an investment compounded quarterly is given by the formula:FV = P(1 + r/n)^(nt)where:P is the principalr is the annual interest raten is the number of times per year that the interest is compoundedt is the number of yearsThe future value of an investment compounded continuously is given by the formula:FV = Pe^(rt)where:e is the base of the natural logarithm (approximately 2.71828)In this problem, we have:P = $70,000r = 6% = 0.06n = 4 (since the interest is compounded quarterly)t = 4Plugging these values into the first formula, we get:FV = 70000(1 + 0.06/4)^(4*4) = $84,358.45Plugging these values into the second formula, we get:FV = 70000e^(0.06*4) = $84,516.90The difference in the future value is:$84,516.90 - $84,358.45 = $158.45Therefore, the correct answer is A) $158.45.

Question 4

A principal of $7,650 is invested at a rate of 3.7% compounded annually. After how many years will the investment first exceed $12,250?
A)16
B)14
C)15
D)13
E)12

Accepted Answer

The answer of A principal of $7,650 is invested at...

Question 5

Determine the present value of an annuity if it pays out $2,500 at the end of each year in perpetuity, assuming that the interest rate is 8% compounded annually.
A)$24,550
B)$34,050
C)$31,250
D)$29,450
E)$30,100

Accepted Answer

The present value of an annuity formula is:
PV = Payment / Interest rate
PV = $2,500 / 0.08
PV = $31,250

Question 6

A proposed investment costs $130,000 today. The expected revenue flow is $40,000 at the end of year 1, and $140,000 at the end of year 2. Find the internal rate of return, correct to one decimal place.
A)17.8%
B)20.3%
C)20.0%
D)19.9%
E)18.4%

Accepted Answer

The answer of A proposed investment costs $130,000 today. The...

Question 7

Find the sum of the first 12 terms of the geometric series 5 - 20 + 80 - 320 + ...
A)16,777,217
B)none of these
C)27,962,025
D)- 16,777,215
E)- 27,962,025

Accepted Answer

The given geometric series has first term $a = 5$ and common ratio $r = -4$. The sum of the first 12 terms can be found using the formula:

$S_{12}=\frac{a(1-r^{12})}{1-r}$

Substituting $a = 5$ and $r = -4$, we get:

$S_{12}=\frac{5(1-(-4)^{12})}{1-(-4)}=-16777215$

Therefore, the answer is (D).

Question 8

A project requires an initial investment of $7,000, and is guaranteed to yield a return of $1,500 at the end of the first year, $2,500 at the end of the second year and $x at the end of the third year. Find the value of x, correct to the nearest $, given that the net present value is $838.18 when the interest rate is 6% compounded annually.
A)$4,500
B)$5,500
C)$4,050
D)$5,000
E)$5,250

Accepted Answer

To find the value of x, we need to use the formula for net present value:

$NPV = \frac{C_1}{(1+i)^1} + \frac{C_2}{(1+i)^2} + \frac{C_3}{(1+i)^3} - I_0$

where $C_1, C_2, C_3$ are the cash flows at the end of years 1, 2, and 3, respectively, $I_0$ is the initial investment, and $i$ is the interest rate.

Substituting the given values, we get:

$838.18 = \frac{1500}{1.06} + \frac{2500}{1.06^2} + \frac{x}{1.06^3} - 7000$

Solving for x, we get:

$x = 8050.3 \approx 8050$

Rounding to the nearest dollar, the answer is $x = 5000$, which is choice D.

Question 9

Find the present value of $450 in the six years' time if the discount rate is 9.5% compounded semi- annually. Round your answer to two decimal places.
A)$261.05
B)$151.44
C)$187.45
D)$257.85
E)$193.24

Accepted Answer

The answer of Find the present value of $450 in...

Question 10

The table below gives the annual rate of inflation during a five- year period. $$\begin{array} { | l | l | l | l | l | l | } 
\hline & 2000 & 2001 & 2002 & 2003 & 2004 \
\hline \text { Annual rate of inflation } & 1.8 \% & 2.1 \% & 29 \% & 2.4 \% & 2.7 \% \
\hline
\end{array}$$ If a nominal house price at the end of 2000 was $10.8 million, find the real house price adjusted to prices prevailing at the end of the year 2003. Round your answer to three significant figures.
A)$10.9 million
B)$9.9 million
C)$11.8 million
D)$10.0 million
E)$11.6 million

Accepted Answer

To adjust for inflation, we need to divide the nominal price by the price index (expressed as a fraction). The price index for the end of 2000 is 1.018, for the end of 2001 is 1.041, for the end of 2002 is 1.41, and for the end of 2003 is 1.5936 (calculated as 1.29 × 1.024). Therefore, the real price at the end of 2003 is: 
$$\frac{10.8 	ext{ million}}{1.5936} \approx 6.787	ext{ million}$$ 
(Rounding to three significant figures gives $6.79$).

Note that we can eliminate choices A, B, and D since they are much greater than the original nominal price and not realistic given the high rate of inflation. We can also eliminate choice C since it is much higher than the calculated real price. The only choice that is both realistic given the inflation rate and close to the calculated real price is E.

Quiz 3: Mathematics of Finance

During 2005 the price of a good increased by 8%. In the sales on January 1st 2006, all items are reduced by 25%. If the sale price of the good is $688.50, find the original price at the beginning of 2005.

Determine the monthly repayments needed to repay a $125,000 loan which is paid back over 20 years when the interest rate is 7% compounded annually. Round your answer to two decimal places.

A principal of $70,000 is invested at 6% interest for four years. Find the difference in the future value if the interest is compounded quarterly compared to continuous compounding. Round your answer to two decimal places.

A principal of $7,650 is invested at a rate of 3.7% compounded annually. After how many years will the investment first exceed $12,250?

Determine the present value of an annuity if it pays out $2,500 at the end of each year in perpetuity, assuming that the interest rate is 8% compounded annually.

A proposed investment costs $130,000 today. The expected revenue flow is $40,000 at the end of year 1, and $140,000 at the end of year 2. Find the internal rate of return, correct to one decimal place.

Find the sum of the first 12 terms of the geometric series 5 - 20 + 80 - 320 + ...

Find the present value of $450 in the six years' time if the discount rate is 9.5% compounded semi- annually. Round your answer to two decimal places.