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Introductory Business Mathematics
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Question 1
Mr. and Mrs. Chan have decided to put some money aside for taking their children to Disney World in 4 years’ time. They explored the website and decided to use the National Australia Bank for the term deposit.
Suppose they intend to deposit $50 000 for 4 years, and found that the bank offers 4 alternatives, each with different interest rates and compounding periods. Using this information, calculate how much has their money grown and what interest was earned in each of the 4 alternatives?
Write at least a 100-word report on this investigation, including the 4 different alternatives and justify which alternative should Mr. and Mrs. Chan choose.
Answer 1
    
    Annually
    Semi annually
    Quarterly
    Monthly
    Interest Rates on
4 years Maturity
    1.00% p.a.
    1.00% p.a.
    1.00% p.a.
    1.00% p.a.
Using the formula for compound interest we calculate the interest and the closing amounts
A= P + (1 + r/n) nt
Case 1 Annually
    Year
    Opening Balance
    Interest Earned
    Closing Balance
    1
    50000
    500
    50500
    2
    50500
    505
    51005
    3
    51005
    510
    51515
    4
    51515
    515
    52030
    Total Interest Earned
    2030
*all figures are in dollars $
Case 2 Semi- Annually
    Year
    Opening Balance
    Interest Earned
    Closing Balance
    1
    50000
    501
    50501
    2
    50501
    506
    51007
    3
    51007
    511
    51518
    4
    51518
    516
    52034
    Total Interest Earned
    2034
*all figures are in dollars $
Case 3 Quarterly
    Year
    Opening Balance
    Interest Earned
    Closing Balance
    1
    50000
    502
    50502
    2
    50502
    507
    51009
    3
    51009
    512
    51521
    4
    51521
    517
    52038
    Total Interest Earned
    2038
*all figures are in dollars $
Case 4 Monthly
    Year
    Opening Balance
    Interest Earned
    Closing Balance
    1
    50000
    502
    50502
    2
    50502
    507
    51009
    3
    51009
    512
    51521
    4
    51521
    518
    52039
    Total Interest Earned
    2039
*all figures are in dollars $
On term deposits of 4 years the National Australian Bank offers an interest rate of 1.00%p.a. on all the compounding periods. Usually the interest rates are different but in term deposit of a maturity of 4 years the interest rates are 1.00% p.a. for all the compounding periods.
The most frequent compounding period offers the highest interest rate. Interest on interest helps to earn more on the principal amount and the greater the number of compounding frequencies the higher the total interest earned. In this case also monthly compounding period gives the highest interest of $2039 and hence monthly compounding term deposit should be chosen.
The Future value is the highest when the compounding is done on monthly basis on term deposit as it will offer maximum return. The future value in case of monthly compounding is $52039.
From our analysis we conclude that the term deposit with monthly compounding should be done for an amount of $50,000 for four years so as to earn the maximum interest amount of $2039 which will lead to the maturity amount of $52039.
Question 2
Another way of managing money is through a savings account. There are different types of savings account that you can consider for depositing your money. Each type will have different variables,...