# Time Value Of Money And Interest Rates

Submitted By Seirim-Tjong
Words: 1320
Pages: 6

Q1. Time Value of Money and Interest Rates
Bank Investment Scenarios
a)
According to the question given David invests \$10,000 in a 6 months term deposit with National Australia Bank. Refer to the term deposit interest rates of National Australia Bank on investment, the 6 months interest rate is 4.15% per annum, compounded annually. Therefore dividing 4.15% by two can get the real interest rate, which is 2.075%.

By using the formula above, which be able to calculate the interest receivable by David after maturity of investment.
David’s investment Scenarios
Principle Amount (\$)
10,000
Period (months)
6
NAB interest rate (%)
4.15
Interest Receivable (\$)
207.50
Maturity Value (\$)
10,207.50

The interest received by David after 6 months will be \$207.50 and the maturity value (principle amount + interest receivable amount) is \$10,207.50.

b)
Refers to the question given, Sofia decides to invest \$10,000 in a term deposit of 90-day with National Australia Bank. The only different between Sofia and David is the period of deposit in the bank different. David chooses the 6 months deposit, however Sofia chooses only 90-day deposit. Because of the time period different, it makes the return investment strategy different.
Now, let’s look at the interest received by Sofia for the first investment. Refer to the term deposit interest rates of National Australia Bank on investment, the 90-days interest rate is 4.10% per annum, compounded annually. Therefore dividing 4.10% by 90day out of 360 days can get the real interest rate, which is 1.011%.Again by using the formula from the question above:

Sofia’s investment Scenarios
Principle Amount (\$)
10,000
Period (days)
90
NAB interest rate (%)
4.10
Interest Receivable (\$)
101.10
Maturity Value (\$)
10,101.10

For the first investment, the interest received by Sofia after 90-days will be \$101.10 and the maturity value (principle amount + interest receivable amount) is \$10,101.10.
Again, Sofia re-invest the Principle \$10,000 in another 90-day term deposit. Assuming the term deposit rates did not change over time. Therefore the calculation for her interest will be the same as the first time.

Interest receivable 1
\$101.10

Interest receivable 2
\$101.10

Interest expected

\$202.20
From the table above, Sofia receives \$202.20 which is less than what David receives for his fixed 6 months term deposit (\$207.50).
c)
The question given that Jack and Sandra both deposited \$10,000 in term deposit with National Australia Bank for period of 9 months and 12 months respectively. The 9 months interest rate with deposits at 3.05% per annum whereas the 12 months interest rate with deposits at 4.20% per annum.
Interest receivable by Jack at maturity of his deposit with NAB = \$10,000 x (3.05% x 9/12) = \$228.75
Jack’s investment Scenarios
Principle Amount (\$)
10,000
Period (months)
9
NAB interest rate (%)
3.05
Interest Receivable (\$)
228.75
Maturity Value (\$)
10,228.75

Interest receivable by Sandra at maturity of her deposit with NAB = 10000 x (4.20% x 12/12) = \$420.00
Sandra’s investment Scenarios
Principle Amount (\$)
10,000
Period (months)
12
NAB interest rate (%)
4.20
Interest Receivable (\$)
420.00
Maturity Value (\$)
10,420.00

At this stage, Jack will be entitled to receive \$10,228.75 for his maturity value and Sandra would be receiving \$10,420.00 for her maturity value.
However, the case given that Jack wishes to earn the same amount at maturity as Sandra which is \$10,420.00. He would like to re-invest the money after completion of 9 months deposit and start another 3 months deposit. To calculate the 3 months interest rate this was required by Jack.
Jack’s maturity value after 9 months is \$10,228.75 which will become the new principal amount for Jack. And he is going to invest for 3 months to match Sandra’s maturity period. Here is the table to show clear about that.
Jack’s re-investment Scenarios