MAP4C Lesson Assignment 16 | Annuities

MAP4C Lesson Assignment 16
In this assignment you are going to focus on: Annuities
Total Marks: 60 marks
Instructions:
After completing the lesson action section of your home page, you are ready to complete your lesson assignment. Follow
these steps.
a) In the textbox given, explain the strategy that you used to determine your answer.
b) Fill in your answer. The mark for each question is given at the introduction to the questions to be completed.
c) When finished answering all your questions, save your file and upload the file into the appropriate dropbox.
Part A (Putting the Concepts to Work): Completion (60 marks): Using your reading, answer the following
questions. Give your answer as well as your strategy for determining your answer (this will include: the information
given in the question, the formula to be used, the calculations and the final answer.
As part of your answer, give the page number in the reference material or the website that you used to find the answer to
the question.
1. (four marks) An amount of $800 is invested at the end of each month for 12 months into an account that pays
3% per year, compounded monthly. Determine the future value of this annuity.
Solution:
PMT= 800, i = 3/12 % = 0.4 %, n = 12
FV = PMT ∗( 1+ i ) n −1
i
FV = $ 9814.04
____ 2. (four marks) An amount of $1500 is deposited semi-annually for two years into a fund that pays 10.5% per
year, compounded semi-annually. Use a TVM Solver to determine the future value of this annuity.
c. $ 6489.25
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a. $6079.21 c. $6489.25
b. $5871.01 d. $3078.75
____ 3. (four marks) Determine the monthly payment for a five-year loan on a $19 000 vehicle at 7% per year,
compounded monthly.
$ 376.22
P = 19000, r = 7% , n =12, Y = 5
PMT = ( P∗r
n )/ [ 1−( 1+ r
n )
−nY
]
PMT = $376.22
4.(four marks) Determine the monthly deposit needed to save $10 000 in three years if interest is earned at 3.5% per year,
compounded monthly.
Solution:
$ 9004.62
A=10000, Y = 3, n =12, r = 3.5%
PMT = (Ar/n) * (1+ r
n )ny
−1
Solving we have,
PMT = $9004.62
5. (four marks) Determine the amount that should be invested now to generate an semi-annual income of $2000
for three years from a fund that earns 9% per year, compounded semi-annually.
PMT = 2000, n = 2*3 = 6 , i = 9/2 % = 4.5%
P=PMT∗[ 1− ( 1+ i )−n
i ]
P = 10315.74
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6. (four marks) Determine the present value of monthly car payments of $590 at 6.9% per year, compounded
monthly for two years.
PMT = 590 , n = 24, i = 6.9/12 % = 0.575 %
PV =PMT∗[ 1− ( 1+i )−n
i ]
( PV ) = $13191.06
7. (four marks) Colin recently started a part-time job. He is saving to travel to Europe. He plans to deposit $500
at the end of each month into an account that pays 2.4% per year, compounded monthly. How much will
Colin have saved at the end of eight months?
PMT= 500, i = 2.4/12 % = 0.2 %, n = 18
FV = PMT ∗( 1+ i )n −1
i
FV = $ 9154.64
8. (four marks) Hayden recently graduated from college and owes $24 000 on a student loan that she must
begin to repay. Payments are to be made at the end of each month for the next five years. Interest is 8.5% per
year, compounded monthly. Calculate the total amount needed to repay the loan.
P = 24000, n =12 , Y = 5 , r = 8.5 %
PMT = ( P∗r
n )/ [ 1−( 1+ r
n )
−nY
]
Monthly payment : 492.40
Total amount needed to pay off the loan : 492.40 * 12 *5 = $29544
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