MCR3U Summative Assignment

Part 2 Annuity and Amortization: Buying a Home

Textbook page references (for additional reading and examples): 129-142

  1. Use your textbook to write definitions for the following terms:

Annuity:

Payment Interval:

Ordinary Annuity:

After finishing school, you decide to begin saving to buy a home. After some careful planning, you decide that you can deposit $3500 into a savings account at the end of each year. The account will earn 6.5% interest, compounded annually.

Complete the table to determine how much money the annuity will be worth after five years.

Year / Balance ($) / Interest Earned in that Year ($) / Payment Made at the End of the Year ($) / New Balance (End of Year) ($)
0 / 0 / 0 / 3500 / 3500
1 / 3500
2
3
4
5
  1. When you find the house or apartment that is right for you, you may be required to take out a loan from a financial institution. You agree to amortize (repay) the value of the loan (principal), plus interest, by making regular equal payments for the term or amortization period. The payment is called a blended payment because part of it is to pay for the interest and the rest to pay down the principal.

When your loan is signed, you will have an amortization table that is a schedule of repayment.

Carry out some independent research into finding a home that you could see yourself purchasing (someday). Some good resources can be local real estate guides (usually found at your local grocery store), newspapers, real estate web sites. When you have chosen your property, cut out or print the details/advertisement and include with this assignment.

Calculating your loan amount:

Principal Loan amount = Purchase price of your home – downpayment saved

(amount calculated in part A)

Your loan will be compounded monthly at the low annual interest rate of 4.69% (r=0.0469) and you will make a blended payment of $953 per month if your loan is less than $180 000, you will make a blended payment of $1400 per month if your loan is between $180 000 and $260 000. (In reality, this payment is calculated based on your loan amount). Your payments are made at the end of the month. Calculate the monthly interest rate: i =

Complete the amortization table below for the first year of paying your loan.

Payment Number / Blended Payment ($) / Interest Paid
= i x the last outstanding balance ($) / Principal Paid = (Blended Payment) – (Interest Paid) ($) / Outstanding Balance ($)
0 / ------/ ------/ ------/ Write your principal loan amount here.
$
1
2
3
4
5
6
7
8
9
10
11
12

In this first year, how much interest will you have paid?

What is your outstanding balance at the end of the first year? How much of your loan have you paid?

Provide complete and neatly organized solutions to the following questions from your textbook.

Page 138-140 #6, 7, 14

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MCR3U Summative Assignment

Criteria / 0.0 2.0 4.0 / Level I
5.0 5.5 / Level II
6.0 6.5 / Level III
7.0 7.5 / Level IV
8.0 9.0 10.0
A. Simple Annuity / Error in the calculation of more than one column.
Definitions not present. / Error in the calculation of an entire column. / Some definitions correct. / Most cells in table are correct.
Definitions mostly correct. / All cells in table correct.
Definitions correct and complete.
B. Ammortization / Error in the calculation of more than two columns.
Information on purchase home not provided.
Questions not answered. / Error in the calculation of two columns.
Error in answers to questions. / Error in the calculation of one column.
Correct answers to questions. / Loan amount correct.
Most cells in table correct.
Correct answers to questions. / Loan amount correct.
All cells in table correct.
Correct answers to questions.
C. Practice Concepts / Incomplete
Solutions provided contain errors. / All solutions are complete but contain numerous errors. / Some solutions are provided but all are correct.
Some correct use of mathematical notation. / All solutions are complete and most are correct.
Mostly correct use of mathematical notation. / All solutions are complete and correct.
Correct use of mathematical notation.

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