Math 1101 chapter 10 review

 

 

  1. Chris just paid off his car.  He calculates that it will last 5 more years.  He would like to save enough money during this time to buy a new car and pay it off entirely.  He is expecting to pay $24,000 for the car.  How much should he put away each month if his interest rate is 7.2% compounded monthly?

This is a future value since he needs 24000 in 5 years.

So we use

24000=71.96473534 R

R = $333.50

 

  1. The cost of tuition at NEI for one year is approximately $12,800.  If an annual increase of 8% is expected, what will be the cost of tuition for one year in 15 years?

This is a compound interest problem.

A = 12800(1 + .08)^15

A = $40603.76

 

  1. Jennifer wants to retire in 40 years.  She puts $300/month into a retirement fund which earns a 9% nominal interest rate.  How much money will she have when she retires?

This is a future value of an annuity.

A = 300[(1.0075)^480 – 1]/.0075

A = $1,404,396.08

 

  1. Chad has $1,000,000 in his retirement account when he retires.  How much money can he withdraw each month if he plans to live for 20 years and his investment earns 6% compounded monthly?

This is a present value problem since he has the $1,000,000 now.

1000000 = R[1-(1.005)^-240]/.005

1000000 = 139.5807717 R

R = $7164.31

 

 

 

  1. Given the following sequence: -5, -9, -13, -17, ...          (3 points each)

A.                 Is the sequence arithmetic or geometric?                                    ____________

                                                                                               

Arithmetic.  The same amount is being added each time

 

B.                 What is the formula for the nth term of the sequence?     ____________

D = -4

                                                                         

 

C.                   What is the 25th term of the sequence?                                            ____________

, this is the better answer.

 

  1. Given the sequence find the sum of the first 15 elements.

 

 

7.      Given the recursively defined sequence:

            find the first four terms of the sequence.

 

 

8.         Given the following sequence: 5, 2.5, 1.25, .625, ...       (3 points each)

A.                 Is the sequence arithmetic or geometric?                                    ____________

Geometric.  There is a common ratio.

 

B.                 What is the formula for the nth term of the sequence?     ____________

 

C.                 What is the 12th term of the sequence?                          ____________

 

 

 

 

 

D.                 Find the sum of the first 12 terms of the sequence.                     ____________

 

 

9.      Find the infinite sum of the sequence: 8, 8/3, 8/9, 8/27, ...         

 

S =