Chapter 7 Flashcards
A sum of $12 800 is invested into an account earning compound interest at the rate of 5.8% per annum.
a.
If there is a choice, should the investor choose weekly compounds or monthly compounds?
b.
Use a spreadsheet or recurrence relation to calculate the difference in interest earned during the first year of investment by monthly and weekly compounds.
a.
Correct Answer
Weekly
b.
Correct Answer
$1.46
Use the rule for the annual percentage interest rate of compound interest loans and investments to determine the interest rate for the following loans and investments after the given period of time. Round your answers to two decimal places.
a.
An investment of $2000.00 earning compound interest that compounds quarterly and with a future value of $2560.67 after 6 years.
c.
An investment of $50 000.00 earning compound interest that compounds monthly and with a future value of $63 828.57 after 4 years.
e.
An investment of $45 000 earning compound interest that compounds weekly and with a future value of $52 153.57 after 3 years.
a.
Correct Answer
4.14%
c.
Correct Answer
6.12%
e.
Correct Answer
4.92%
A reducing-balance loan with interest compounding monthly and with monthly repayments can be modelled by the recurrence relation
A0=14 500, An+1=1.0072×An−1500
where An is the balance of the loan after n repayments have been made.
a.
Calculate the annual percentage rate of interest.
b.
Use calculator recursion to determine how much is owed on the loan after three months.
c.
How much interest has been paid after three months?
a.
Correct Answer
8.64%
b.
Correct Answer
$10 282.98
c.
Correct Answer
$282.98
Andrea needs to borrow $20 000. Her bank will charge interest at the annual percentage interest rate of 7.08%, compounding monthly. Andrea will be required to make monthly repayments of $600, but Andrea thinks she can afford to pay $800 instead.
a.
Construct a recurrence relation model for the loan with monthly repayments of $600 and apply it to evaluate:
i.
how much Andrea would owe after five months
ii.
the total interest that Andrea would pay after five months
b.
Construct a recurrence relation model for the loan with monthly repayments of $800 and apply it to evaluate:
i.
how much Andrea would owe after five months
ii.
the total interest that Andrea would pay after five months
c.
If Andrea makes monthly repayments of $800 instead of $600, how much interest will she save over the first five months of her loan?
a.
i.
Correct Answer
A0=20000,An+1=1.0059An−600
$17 561.39
b.
Correct Answer
A0=20000,An+1=1.0059An−600
$561.39
b.
i.
Correct Answer
A0=20000,An+1=1.0059An−800
$16 549.52
ii.
Correct Answer
A0=20000,An+1=1.0059An−800
$549.52
c.
Correct Answer
$11.87
Misaki borrowed $8400 and will be charged compounding interest at the rate of 11.4% per annum, compounding monthly. Misaki will make monthly repayments of $500.
a.
Construct a repayment schedule to determine the balance of Misaki’s loan after five repayments.
b.
How much interest in total has Misaki paid after five repayments?
Correct Answer
$358.70
Vadik borrowed $2000 and will be charged compounding interest at the rate of 18.2% per annum, compounding weekly. Vadik will make weekly repayments of $100.
a.
Construct a repayment schedule to determine the balance of Vadik’s loan after five repayments.
b.
How much interest in total has Vadik paid after:
i.
three weeks?
ii.
four weeks?
b.
i.
Correct Answer
$20.02
ii.
Correct Answer
$26.04
Sofia borrowed $4600 and will be charged compounding interest at the rate of 4.8% per annum, compounding monthly. The first three repayments that Sofia made were for $300. The next two repayments Sofia made were for $450.
Construct a repayment schedule to determine the balance of Sofia’s loan after five repayments
Sofia borrowed $4600 and will be charged compounding interest at the rate of 4.8% per annum, compounding monthly. The first three repayments that Sofia made were for $300. The next two repayments Sofia made were for $450.
Construct a repayment schedule to determine the balance of Sofia’s loan after five repayments
