Section D Section D Checkpoint

Problem 1

A large field used to be sprayed so that only grass would grow. A new owner wants wildflowers to grow, so they stop spraying the field. The first year after not spraying there are 1,000 wildflowers in the field. Each month, the number of wildflowers increases by 10%.

If this pattern holds for 6 months, will there be 60% more wildflowers in the field? Explain your reasoning.

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Solution

No, there will be more than 60% more wildflowers. Sample reasoning: The increase is compounding, so the increase each month comes from the original 1,000 wildflowers as well as any flowers that grew in the previous months.

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Sample Response

Problem 2

An investor has two options for a savings account. To determine which is the better deal, the investor imagines investing $2,000 and making no deposits or withdrawals for 5 years.

Bank 1: 3% nominal annual interest compounded monthly
Bank 2: 3% nominal annual interest compounded quarterly

How much would be in each account at the end of the 5 years? Show your reasoning.
Which bank should the investor choose?

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Solution

Sample responses:

Bank 1: $2,323.23 because $\frac{0.03}{12} = 0.0025$ , and $2000 \boldcdot (1 + 0.0025)^{60} = 2323.23$ .
Bank 2: $2,322.37 because $\frac{0.03}{4} = 0.0075$ , and $2000 \boldcdot (1 + 0.0075)^{20} = 2322.37$
The investor should choose Bank 1 because with the same initial deposit and interest, the account that compounds more often will result in more money.

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Sample Response

Sample responses:

Bank 1: $2,323.23 because $\frac{0.03}{12} = 0.0025$ , and $2000 \boldcdot (1 + 0.0025)^{60} = 2323.23$ .
Bank 2: $2,322.37 because $\frac{0.03}{4} = 0.0075$ , and $2000 \boldcdot (1 + 0.0075)^{20} = 2322.37$
The investor should choose Bank 1 because with the same initial deposit and interest, the account that compounds more often will result in more money.