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```Investment Opportunities
Individual Option
2 year CD vs. 5 year CD
Company Name:
GE Capital Bank
 1.15% interest rate
 Minimum Investment:
\$500

Company Name:
GE Capital Bank
 2.00% interest rate
 Minimum Investment:
\$500

Functions of Plans
2 Year CD Plan
f(x) = 5000(1.0115)^x
5 Year CD Plan
f(x) = 5000(1.0200)^x
Function for Investor’s Plan
f(x) = 5000 + 50x
Proposed Profits of Plans
Plan
Function
Year 1
Year 2
Year 3
Year 4
Year 5
2 Year CD
f(x) =
5000(1.0115)^x
\$5057.50
\$5115.66
\$5174.49
\$5234.00
5294.19
5 Year CD
f(x) =
5000(1.0200)^x
\$5100.00
\$5202.00
\$5306.04
\$5412.16
\$5520.40
Investor
f(x) =
5000 + 50x
\$5050.00
\$5100.00
\$5150.00
\$5200.00
\$5250.00
Linear vs. Exponential
The Investor’s plan is a linear function
because it is a slope intercept based function
of f(x) = 50x + 5000, where the x variable is
never brought to an exponent higher than 1.
The 5 year CD and 2 year CD are
exponential functions because the interest
rate is multiplied by an exponent variable
representing the number of years paid on the
investment.
Average Rate of Change
Five Year CD Plan
f(3) – f(2)
3-2
5000(1.02)^3 – 5000(1.02)^2
1
5306.04 – 5202
1
\$104.04
f(5)-f(3)
5-3
5000(1.02)^5 – 5000(1.02)^3
2
5520.40 - 5306.04
2
214.36
2
\$107.18
This shows that in the long run the 5 Year CD plan would be the
most lucrative. The Investor’s plan would earn more between
the years of 2 and 3, but afterward it would make more than 50\$
less per year than the 5 year CD plan.
Investor’s Plan
f(3) – f(2)
3-2
{5000 + 50(3)} – {5000+50(2)}
1
5150 – 5100
1
\$ 150.00
f(5) – f(3)
5-3
{5000+50(5)} – {5000+50(3)}
2
5250 – 5150
2
100
2
\$50.00
Alternate Proposal
1.02 in the function represents a 2.00%
investment rate. This plan that you proposed
is the same plan as the 5 year CD plan I
presented to you. Your plan is neither better
nor worse in terms of creating a profit. The
outcome will be the same.
Conclusion
In conclusion, I believe we should follow
the 5 Year CD plan. This plan will make in 5
years at least \$225 more than the next best
plan (the 2 year CD plan). The waiting for the
5 Year CD plan to fully mature is the option
that will have the most benefit in the form of
the largest profit.
```
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