Question

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

Answer 1

Answer:

The approximate difference in time is 2 years.

Step-by-step explanation:

The equation for Calvin's account is

$658.80=400(1+\frac{0.05}{12})^{12c}$

To solve for c, we first divide both sides by 400.  This gives us:

$1.647=(1+\frac{0.05}{12})^{12c}$

Using logarithms to solve this, we have

$\log_{1+\frac{0.05}{12}}1.647=12c\\\\119.9986131=12c$

Dividing both sides by 12, we get c = 9.9998 or around 10 years.

The equation for Makayla's account is

$613.04=300(1+\frac{0.06}{4})^{4m}$

Dividing both sides by 300, we get

$2.043466667=(1+\frac{0.06}{4})^{4m}$

Using logarithms to solve this, we have

$\log_{1+\frac{0.06}{4}}2.043466667=4m\\\\4m=47.9961799$

Dividing both sides by 4, we get

m = 11.9999 or about 12.

This means Makayla had her money in the account 12-10 = 2 years longer than Calvin.

Answer 2

Answer:

It is B makayla invest her money 2 yrs longer

Step-by-step explanation:

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