Question 1

What is the present value of a lottery prize of 2 million dollars, paid out at a rate of $40,000 per year for 50 years? Assume an annual interest rate of 3%. Round to the nearest dollar.

Accepted Answer

$1,060,066

Question 2

A patient takes 400 mg of a pain-killing drug twice a day. Every 12 hours, the patient's body metabolizes 20% of the drug present. If the patient continues to take the drug indefinitely, how many mg of the drug will remain in the patient's body in the long run? Round to 2 decimal places.

Accepted Answer

2000.00

Question 3

Find the sum of the series  , for
 .
A) 
B) 
C) 
D)

Accepted Answer

A

Question 4

What is   ? Round to 2 decimal places.

Accepted Answer

The answer of What is   ? Round to...

Question 5

Subtract the following two equations and solve for S:  Assume x is not equal to 1.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Subtract the following two equations and solve...

Question 6

Let , with  . As , what happens to S?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Let , with  . As ,...

Question 7

An athlete is offered a signing bonus of $2 million per year for 7 years. If the interest rate is 4% per year, compounded annually, what is the present value of this bonus? Round to the nearest dollar.

Accepted Answer

The answer of An athlete is offered a signing bonus...

Question 8

A plaintiff is awarded a settlement of $15,000 per year (paid at the beginning of the year) for the rest of his life. Assuming 3.7% annual interest, how much money would the defendant have to put aside now in order to ensure that the settlement would be paid (no matter how many years the plaintiff lived)? In other words, what is the present value of the settlement if the plaintiff may live indefinitely? Round to the nearest dollar.

Accepted Answer

The answer of A plaintiff is awarded a settlement of...

Question 9

Does the infinite geometric series  
converge or diverge?

Accepted Answer

The answer of Does the infinite geometric series  
converge...

Question 10

Write   as a fraction.

Accepted Answer

The answer of Write   as a fraction....

Question 11

An employee is offered a salary of $100,000 per year for 6 years. What is the present value of the contract on the date of the first payment if the interest rate is 2.3% per year, compounded continuously. Round your answer to two decimal places.

Accepted Answer

The answer of An employee is offered a salary of...

Question 12

Write   as a fraction.

Accepted Answer

The answer of Write   as a fraction....

Question 13

What is the present value of a $1000 bond which pays $40 each year for 15 years, with the first payment one year from now? Assume the interest rate is 5.1% per year compounded annually.

Accepted Answer

The answer of What is the present value of a...

Question 14

What is the present value of a $1000 bond which pays $45 each year for 15 years, with the first payment one year from now? Assume the interest rate is 5.5% per year compounded annually.
A) $899.62
B) $451.69
C) $904.10
D) $895.38

Accepted Answer

The present value of the bond is calculated by discounting the annual coupon payments and the face value of the bond at the given interest rate. The present value of the coupon payments is calculated using the formula for the present value of an annuity, and the present value of the face value is calculated using the formula for the present value of a single sum. The sum of these two present values gives the total present value of the bond, which is $899.62.

Question 15

Find the sum   . Round your answer to 3 decimal places.

Accepted Answer

The answer of Find the sum   . Round...

Question 16

Your doctor tells you to take 37 mg of a certain drug every 12 hours. It is known that only 6% of the drug is still in the body at the end of 12 hours. What quantity of the drug is in the body right after taking the 11th dose? Give your answer correct to 3 decimal places.

Accepted Answer

The answer of Your doctor tells you to take 37...

Question 17

Your doctor tells you to take 38 mg of a certain drug every 12 hours. It is known that only 6% of the drug is still in the body at the end of 12 hours. Assuming you continue to take the drug, what happens to the drug level in the long run? Give your answer correct to 3 decimal places.

Accepted Answer

The answer of Your doctor tells you to take 38...

Question 18

For what values of x does the sum  converge?

Accepted Answer

The answer of For what values of x does the...

Question 19

For what values of x does the sum  converge?

Accepted Answer

The answer of For what values of x does the...

Question 20

Find the sum of the series:

Accepted Answer

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

Quiz 13: Sequences and Series

What is the present value of a lottery prize of 2 million dollars, paid out at a rate of $40,000 per year for 50 years? Assume an annual interest rate of 3%. Round to the nearest dollar.

A patient takes 400 mg of a pain-killing drug twice a day. Every 12 hours, the patient's body metabolizes 20% of the drug present. If the patient continues to take the drug indefinitely, how many mg of the drug will remain in the patient's body in the long run? Round to 2 decimal places.

Find the sum of the series , for .

What is ? Round to 2 decimal places.

Subtract the following two equations and solve for S: Assume x is not equal to 1.

Let , with . As , what happens to S?

An athlete is offered a signing bonus of $2 million per year for 7 years. If the interest rate is 4% per year, compounded annually, what is the present value of this bonus? Round to the nearest dollar.

Does the infinite geometric series converge or diverge?

Write $Write as a fraction.$ as a fraction.