Mathematics, 29.12.2019 15:31 omarabady

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. after c years, calvin has $658.80. makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. after m years, makayla has $613.04. what is the approximate difference in the number of years that calvin and makayla have their money invested?

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Answer from: paulandigi

The approximate difference in the number of years that Calvin and Makayla have their money invested is 2 years.

Given information:

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly.

After c years, Calvin has $658.80.

Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04.

Using the formula of compound interest, the value of c in years can be calculated as,

$A=P(1+\dfrac{r}{n})^{nc}\\658.80=400\times (1+\dfrac{0.05}{12})^{12c}\\(1+\dfrac{0.05}{12})^{12c}=1.647\\c\approx 10\rm\; years$

So, Calvin has invested $400 for about 10 years.

Similarly, the value of m in years can be calculated as.

$A=P(1+\dfrac{r}{n})^{nm}\\613.04=300\times (1+\dfrac{0.06}{4})^{4m}\\(1+\dfrac{0.06}{4})^{4m}=2.04346\\m\approx 12\rm\; years$

So, the approximate difference in the number of years that Calvin and Makayla have their money invested will be 12-10=2 years.

Therefore, the approximate difference in the number of years that Calvin and Makayla have their money invested is 2 years.

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Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. after c years

Answer from: darkghostmist

You will need a special formula to compute this.
Years = log (total/principal) / [n * log * (1 + rate / n)]

Part A) Calvin $400 5% monthly 658.80 Time = ?
Monthly compounding "n" = 12
Years = log(658.80/400) / [12 * log(1+ (.05/n))
Years = log ( 1.647 ) / (12 * log ( 1.0041666667 )
Years = 0.21669359917 / 12 * 0.0018058008777
Years = 0.21669359917 / 0.0216696105
Years = 9.999884362

Part B) Makayla 300 6% quarterly 613.04Time=?
Quarterly compounding
n = 4
Years = log (total/principal) / [n * log * (1 + rate / n)]
Years = log (613.04/300) / [4 * log (1 + .06/4)]
Years = log ( 2.0434666667 ) / 4 * log (1.015)
Years = 0.31036755784 / 4 * 0.0064660422492
Years = 0.31036755784 / 0.025864169
Years = 11.9999044949

So, the difference is roughly 3 years.

Answer from: Quest

What are the options for plato

Answer from: Quest

The answer is part a: use

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