After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth

Mathematics

1 answer:

Irina-Kira [14]3 years ago

5 0

9514 1404 393

Answer:

19 years

Step-by-step explanation:

The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...

A = P(1 +r/n)^(nt)

Solving for t, we get ...

t = log(A/P)/(n·log(1 +r/n))

Using the given values, we find t to be ...

t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000

The investment will be worth $213,022 after 19 years.

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Calculate the length of the side of the square to 1dp.

Sveta_85 [38]

Answer:

72 cm

Step-by-step explanation:

You can solve this problem using the properties of the 45-45-90 right triangle. Assuming the 12 cm is a diagonal of the square, each side of the square can be modeled as x, and the diagonal will be x $\sqrt{2}$ .

This means $x\sqrt{2} =12$ , so $x=\frac{12}{\sqrt{2} }$ .

Next, to find the area of the square you take the square of any of its sides. Since x is the length of one side, and $x=\frac{12}{\sqrt{2} }$ , you can square $\frac{12}{\sqrt{2} }$ to get the area. This is equal to $\frac{144}{2}$ or 72 cm.