For Investment 1, the model polynomial is:
C(x) = 4000(1+r)^7
For Investment 2, the model polynomial is:
C(x) = 2000(1+r)^7 + 1500(1+r)^5 + 500(1+r)^3
To compare the interest earned at the end of the 7-year term for an annual interest rate of 3.7 percent, we substitute r = 0.037 into the model polynomials.
For Investment 1:
C(x) = 4000(1+0.037)^7 = 4000(1.037)^7 ≈ 4889.56
For Investment 2:
C(x) = 2000(1+0.037)^7 + 1500(1+0.037)^5 + 500(1+0.037)^3 ≈ 5020.26
Therefore, Investment 2 will result in more interest earned at the end of the 7-year term if the annual interest rate is 3.7 percent.
When having the same interest rate and investment term, it will be better to invest more at one time rather than dividing the investment into smaller deposits each year. This is because compounding interest benefits from investing larger amounts upfront. In Investment 1, where $4,000 is deposited at the beginning of the first year, the final amount is higher than in Investment 2, where smaller amounts are deposited at different intervals.
Use x=1+r
, where r is the interest rate paid each year. Write a model polynomial, C(x)
, to represent the final amount of each of the following 7-year term investments.
Investment 1: Deposit $4,000 at the beginning of the first year.
Investment 2: Deposit $2,000 at the beginning of the first year, $1,500 at the beginning of the third year, and $500 at the beginning of the fifth year.
Using the models that you just created, which investment option will result in more interest earned at the end of the 7-year term if the annual interest rate is 3.7 percent?
Based on the answer you got for this problem, when having the same interest rate and investment term, do you think it will be better to invest more at one time or divide the investment into smaller deposits each year? Explain your reasoning.
(4 points)
1 answer
1 answer