Question 1

Find the sum of the geometric series: 1 +  
+  
  
+  
  
+

Accepted Answer

The answer of Find the sum of the geometric series:...

Question 2

Suppose a company establishes a sinking fund to replace equipment that has a salvage value of $50,000.The company deposits $20,000 into the fund at the end of every six months.If interest is earned at the rate of 8% compounded semiannually,the value of the fund at the end of six years is
A) $137,701.48.
B) $187,701.48.
C) $237,701.48.
D) $250,516.10.
E) $300,516.11.

Accepted Answer

The answer of Suppose a company establishes a sinking fund...

Question 3

$200 is invested at the rate of 3.5% compounded quarterly for six and a half years.How many terms are in the geometric sequence formed by the amounts at the end of each quarter?

Accepted Answer

The answer of $200 is invested at the rate of...

Question 4

A company earns a profit of $5000 in its first month.Suppose its profit decreases by 10% each month for one year.Find the amount of profit the company earns in its first year.

Accepted Answer

The answer of A company earns a profit of $5000...

Question 5

A ball rebounds  
of its previous height after each bounce.If the ball is dropped from a height of 20 meters,how far has it traveled in the air when it hits the ground for the sixth time?

Accepted Answer

The answer of A ball rebounds  
of its previous...

Question 6

Find the present value of an annuity of $200 per month for  
years at an interest rate of 7% compounded monthly.

Accepted Answer

The answer of Find the present value of an annuity...

Question 7

A ball rebounds  
of its previous height after each bounce.If the ball is dropped from a height of 27 feet,how far has it traveled in the air when it hits the ground for the twentieth time?

Accepted Answer

The answer of A ball rebounds  
of its previous...

Question 8

A rubber ball always bounces back  
of its previous height.If the ball is thrown up to a height of 30 feet,give the first five heights of the ball.

Accepted Answer

The answer of A rubber ball always bounces back ...

Question 9

Suppose $500 is initially placed in a savings account that earns interest at the rate of 8% compounded semiannually.Thereafter,$500 is deposited in the account at the end of every six months for five years.The value of the account at the end of five years is
A) $4055.45.
B) $4555.45.
C) $6003.05.
D) $6743.18.
E) $6799.78.

Accepted Answer

The answer of Suppose $500 is initially placed in a...

Question 10

$200 is invested at the rate of 4.5% compounded semiannually for 8 years.Find the compound amounts at the end of the 2nd,4th,and 8th years.

Accepted Answer

The answer of $200 is invested at the rate of...

Question 11

A ball rebounds  
of its previous height after each bounce.If the ball is tossed up to a height of 16 feet,how far has it traveled in the air when it hits the ground for the fifteenth time?

Accepted Answer

The answer of A ball rebounds  
of its previous...

Question 12

$200 is invested at the rate of 6% compounded monthly for 5 months.List the compound amounts at the end of each month as a geometric sequence.

Accepted Answer

The answer of $200 is invested at the rate of...

Question 13

Find the sum of the geometric series: 1 + 2 +  
+ ...+

Accepted Answer

The answer of Find the sum of the geometric series:...

Question 14

A company earns a profit of $2000 in its first month.Suppose its profit increases by 10% each month for two years.Find the amount of profit the company earns in its sixth and sixteenth months.

Accepted Answer

The answer of A company earns a profit of $2000...

Question 15

Consider the following annuity: $2000 due at the end of each year for two years,and $3000 due thereafter at the end of each year for three years.At an interest rate of 4% compounded annually,the present value of the annuity is
A) $12,487.24.
B) $11,469.37.
C) $10,541.31.
D) $10,211.37.
E) $9,583.28.

Accepted Answer

To solve the problem, we can use the formula for the present value of an annuity:

PV = A * [1 - (1+r)^(-n)]/r

where PV is the present value, A is the periodic payment, r is the interest rate per period, and n is the number of periods.

For the first two years, the payments are $2000 each, so we can use:

PV1 = 2000 * [1 - (1+0.04)^(-2)]/0.04 = $3,952.32

For the next three years, the payments are $3000 each, so we can use:

PV2 = 3000 * [1 - (1+0.04)^(-3)]/0.04 = $8,517.05

The total present value is the sum of these two present values:

PV = PV1 + PV2 = $3,952.32 + $8,517.05 = $12,469.37

Therefore, the best choice is B.

Question 16

Suppose a corporation pays $50,000 for a machine that has a useful life of eight years and a salvage value of $5000.A sinking fund is established to replace the machine at the end of 8 years.The replacement machine will cost $70,000.If equal payments are made into the fund at the end of every 6 months and the fund earns interest at the rate of 10% compounded semiannually,what should each payment be?

Accepted Answer

The answer of Suppose a corporation pays $50,000 for a...

Question 17

Suppose a person invests $20,000 in a business venture that guarantees the same cash flow at the end of every quarter for four years.If the investment earns interest at the rate of 16% compounded quarterly,then each cash flow is
A) $916.40.
B) $1527.52.
C) $1716.40.
D) $1917.39.
E) $2341.23.

Accepted Answer

The answer of Suppose a person invests $20,000 in a...

Question 18

A company repays a $50,000 loan by paying 10% of the outstanding loan each month.How much has the company paid back after two years?

Accepted Answer

The answer of A company repays a $50,000 loan by...

Question 19

A company repays a $50,000 loan by paying 10% of the outstanding loan each month.Find the amount the company pays in the fourth and twentieth months.

Accepted Answer

The answer of A company repays a $50,000 loan by...

Question 20

Find the amount of an annuity of payments of $150 at the end of every month for 3 years at the rate of 4% compounded monthly.Also find the compound interest.

Accepted Answer

The answer of Find the amount of an annuity of...

Quiz 6: Mathematics of Finance

Find the sum of the geometric series: 1 + + + +

Suppose a company establishes a sinking fund to replace equipment that has a salvage value of $50,000.The company deposits $20,000 into the fund at the end of every six months.If interest is earned at the rate of 8% compounded semiannually,the value of the fund at the end of six years is

$200 is invested at the rate of 3.5% compounded quarterly for six and a half years.How many terms are in the geometric sequence formed by the amounts at the end of each quarter?

A company earns a profit of $5000 in its first month.Suppose its profit decreases by 10% each month for one year.Find the amount of profit the company earns in its first year.

A ball rebounds of its previous height after each bounce.If the ball is dropped from a height of 20 meters,how far has it traveled in the air when it hits the ground for the sixth time?

Find the present value of an annuity of $200 per month for years at an interest rate of 7% compounded monthly.

A ball rebounds of its previous height after each bounce.If the ball is dropped from a height of 27 feet,how far has it traveled in the air when it hits the ground for the twentieth time?

A rubber ball always bounces back of its previous height.If the ball is thrown up to a height of 30 feet,give the first five heights of the ball.

Suppose $500 is initially placed in a savings account that earns interest at the rate of 8% compounded semiannually.Thereafter,$500 is deposited in the account at the end of every six months for five years.The value of the account at the end of five years is

$200 is invested at the rate of 4.5% compounded semiannually for 8 years.Find the compound amounts at the end of the 2nd,4th,and 8th years.

A ball rebounds of its previous height after each bounce.If the ball is tossed up to a height of 16 feet,how far has it traveled in the air when it hits the ground for the fifteenth time?

$200 is invested at the rate of 6% compounded monthly for 5 months.List the compound amounts at the end of each month as a geometric sequence.

Find the sum of the geometric series: 1 + 2 + + ...+

A company earns a profit of $2000 in its first month.Suppose its profit increases by 10% each month for two years.Find the amount of profit the company earns in its sixth and sixteenth months.

Consider the following annuity: $2000 due at the end of each year for two years,and $3000 due thereafter at the end of each year for three years.At an interest rate of 4% compounded annually,the present value of the annuity is

Suppose a person invests $20,000 in a business venture that guarantees the same cash flow at the end of every quarter for four years.If the investment earns interest at the rate of 16% compounded quarterly,then each cash flow is

A company repays a $50,000 loan by paying 10% of the outstanding loan each month.How much has the company paid back after two years?

A company repays a $50,000 loan by paying 10% of the outstanding loan each month.Find the amount the company pays in the fourth and twentieth months.

Find the amount of an annuity of payments of $150 at the end of every month for 3 years at the rate of 4% compounded monthly.Also find the compound interest.