澳洲国立大学国外金融基础的联系题和答案

Show how and discuss why your answer would change if interest were compounded annually. To work how much you borrowed, simply calculate the present value of all repayments. As payments are evenly spaced and identical in amount, we can calculate the present value of the cash flows using the ordinary annuity formula: 0.10 −180 1 − (1 + 12 ) PV = $2,500 0.10 12 = $232, 643.59 If the interest rate were compounded annually, the amount you borrowed would be higher as there is less compounding of interest and a larger portion of repayments pertaining to the principal. The amount borrowed with annual compounding is calculated as follows:
1
FINM7006: Foundations of Finance r = (1.10)12 − 1 = 0.0079741 1 − (1.0079741)−180 PV = $2, 500 0.0079741 = $238, 461, 46 Question Three Calculate the present value of an ordinary perpetuity that comprises one cash flow of $50 at the end of each year given an interest rate of 9% p.a. compounded annually. Show how and discuss why your answer would change if interest were compounded weekly. $50 0.09 = $555.56
PV =
$50 0.09 52 ((1 + ) − 1) 52 = $531.41
Question Four What would be the balance of my bank account exactly 3 years from today if I made deposits in the account as described below and earned interest at a rate of 10% p.a. compounded annually on my account balance: Time (from today) Amount 1 year $50 2 years $100 3 years $150
• • •
Your monthly repayments are $2,500; The loan is taken over 15 years; and, The interest rate you will pay on funds borrowed is fixed at 10% p.a. compounded monthly.
FV = $500(1 +
= $745.87 Question Two You have just successfully applied for a home loan. Calculate how much you are borrowing given that the terms of the loan are as follows:
FINM7006: Foundations of Finance
Tutorial 2 Solutions
Question One Calculate the future value of $500 invested today for a period of 4 years at an interest rate of 10% p.a. compounded annually. Show how and discuss why your answer would change if interest was compounded daily. The future value of this amount given the interest rate compounds annually is $732.05, and is calculated as follows:
FV = $50(1 +
Textbook Questions Question 7
'Mad Dog' McNamara wishes to accumulate $9,500 at the end of three years. How much does he need to deposit now if the interest rate is
Show how and discuss why your answer would change if interest were compounded daily. As the cash flows are of different sizes, I have to compound each cash flow individually and sum the resultant values in order to calculate the balance of my bank account 3 years from today: 2
1
PV =
If interest rates were compounded weekly, the present value of the perpetuity would be lower due to the increased effects of compounding. The present value of the perpetuity if interest were compounded weekly is:
PV =
FV
(1 + r )
n
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=
9500 = $7, 470.01 1.006736
The answer to (b) is greater than the answer to (a) because the interest rate is lower. The deposit will not earn as much interest under the scenario in part (b), so more needs to be deposited in order to grow to the desired amount. The answer to (c) is less than the answer to (b) because interest is compounded more frequently. This means that the deposit earns ‘interest on interest’ more often. More frequently throughout the year, interest is calculated and added to the deposit, which means that next time interest is calculated it is calculated on
3
FINM7006: Foundations of Finance a larger amount. As a result, less needs to be deposited in order to grow to the desired amount. Question 12
An investment repays $40,000 in 5 years and a further $60,000 in 10 years. If the interest rate over the period of the investment is 12% p.a. compounded monthly, what is the investment's present value?
Whenever you have a problem involving multiple cash flows, it is often advisable to draw a diagram showing all cash flows and identifying the value to be calculated. PV? 0 1 2 3 4 40,000 5 6 7 8 9 60,000 10
(a) (b) (c)
10% per annum compounded annually? 8% per annum compounded annually? 8% per annum compounded monthly?
Can you explain why the amounts differ in each case?
FV = $500(1.10) 4 = $732.05 If the interest rate was compounded daily, the future value of the investment would be greater given the increased impact of compounding. The future value of the investment with daily compounding is calculated as follows: 0.10 4 x 365 ) 365
FINM7006: Foundations of Finance
FV = $50(1.10)2 + $100(1.10) + $150 = $320.50 If interest was compounded daily, my account balance would be higher 3 years from today given the increased impact of compounding: 0.10 2 x 365 0.10 365 ) + $100(1 + ) + $150 365 365 = $321.58
We need to find the present value of the future amount of $9,500. (a)
PV =
(1 + r )
FV
FV
n
=
9500 = $7,137.49 1.10 3 9500 = $7,541.41 1.08 3
(b) (c)
PV =
(1 + r )
n
=
With monthly compounding, the interest rate must be divided by 12 to find the interest rate per compounding period (r), and the number of years must be multiplied by 12 to find the total number of periods (n).