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Paul has €80000 that he wants to invest for a maximum of 3 years - Leaving Cert Mathematics - Question 7 - 2016
Question 7
Paul has €80000 that he wants to invest for a maximum of 3 years. His local bank is offering him two options, Option 1 and Option 2, as shown in the table below. | ... show full transcript
Worked Solution & Example Answer:Paul has €80000 that he wants to invest for a maximum of 3 years - Leaving Cert Mathematics - Question 7 - 2016
Step 1
Find the value of the investment at the end of 3 years if Paul chooses Option 1 and does not take any money out.
Answer
To calculate the value of the investment at the end of 3 years using Option 1, we can apply the formula for compound interest for each year:
-
Year 1:
Amount after Year 1 = €80000 × (1 + 0.02) = €80000 × 1.02 = €81600
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Year 2:
Amount after Year 2 = €81600 × (1 + 0.03) = €81600 × 1.03 = €84048
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Year 3:
Amount after Year 3 = €84048 × (1 + 0.05) = €84048 × 1.05 = €88250.40
Thus, the value of the investment at the end of 3 years if Paul chooses Option 1 and does not take any money out is €88250.40.
Step 2
Find the value of the investment at the end of 3 years if Paul chooses Option 2.
Answer
For Option 2, to find the value of the investment at the end of 3 years with a compound interest of 3-7%, let’s assume an average rate of 5%.
Using the compound interest formula:
v = P(1 + r)^t = €80000(1 + 0.05)^3
Calculating:
= €80000 × (1.157625) = €92610.08
So, if Paul chooses Option 2, the value of the investment at the end of 3 years would be approximately €92610.08.
Step 3
Give one issue, other than the rate of interest earned, that Paul might take into account when deciding between Option 1 and Option 2.
Answer
One issue Paul might consider is the flexibility of accessing his funds. With Option 1, he can take out money at the end of Year 1 or Year 2 without penalty, which provides him with greater liquidity compared to Option 2, where he cannot access his funds until the end of Year 3.
Step 4
Paul would like his investment of €80000 to amount to €90000 after 3 years. What annual rate of compound interest would be required for this to happen?
Answer
To find the required annual rate of interest, we can use the compound interest formula:
given:
grows to €90000 in 3 years:
Let r be the rate in decimal format:
1 + r =
=
Thus,
Solve for r:
1 + r = 90000/80000=1.125 Thus:
Then r = 0.125 or 12.5% in percentages.
Step 5
Find the value of the money in the fund after 12 months.
Answer
Using the formula:
v = 80000 + 36(12) - 1.2(12)^2 Calculating gives us:
v = 80000 + 432 - 1.2(144) v = 80000 + 432 - 172.8 v = 80000 + 259.2 v = €80259.20 Therefore, the value of the money in the fund after 12 months is €80259.20.
Step 6
Find the value of r, correct to 2 decimal places.
Answer
Given: Mary invests €80000 for 1 year at r% per annum.
At the end of the year, her investment is equal to the amount found in part (e)(i): So, we equate:
80000(1 + r/100) = 80259.20 Solving for r:
1 + r/100 = 80259.20 / 80000 r/100 = 80259.20 / 80000 - 1 dividing: r = 100*(80259.20 / 80000 - 1) r = 100*(1.03249 - 1) r = 100*0.03249 = 3.25 to 2 decimal places it is, r = 3.25%.