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kykrilka [37]
3 years ago
9

How much should you invest at 5% simple interest in order to earn $100 interest in 12 months?​

Mathematics
1 answer:
marissa [1.9K]3 years ago
7 0

Answer:

You should invest $2000 at 5% simple interest in order to earn $100 interest in 12 months.

Step-by-step explanation:

Using the formula

I = Prt

where

I = Interest earned

P = The principal (let say in $)

r = The Interest Rate

t = time

Given that

  • I = $100
  • r = 5%
  • t = 12 month = 1 year
  • P = The principal amount needed to invest (let say in $)

Thus,

I = Prt

100 = P × 5% × 1

100 = P × 5/100 × 1

100 × 100 = P × 5

10000 = P × 5

P = 10000/5

  = 2000 (let say in $)

Thus, you should invest $2000 at 5% simple interest in order to earn $100 interest in 12 months.

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Answer:

x = 10/√2 ≈ 7.07

Step-by-step explanation:

Comenzaremos por dividir el triángulo en dos partes y definir H, como en la figura adjunta.

Aplicando el teorema de Tales, sabemos que:

\dfrac{l/2}{H}=\dfrac{x/2}{h}\\\\\\\dfrac{l}{H}=\dfrac{x}{h}

También sabemos que, dado que el tirángulo menor es la mitad que el triángulo mayor, la relación entre áreas es:

\dfrac{A}{A_x}=\dfrac{lH/2}{xh/2}=\dfrac{lH}{xh}=2

Dado que formamos dos triángulos rectángulos, podemos despejar el valor de H como:

(l/2)^2+H^2=l^2\\\\H^2=l^2-(l/2)^2=10^2-5^2=100-25=75\\\\H^2=\sqrt{75}

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h=\dfrac{H}{l}\cdot x=\dfrac{lH}{2x}\\\\\\2x^2\dfrac{H}{l}=lH\\\\\\2x^2=l^2\\\\\\x=\dfrac{l}{\sqrt{2}}=\dfrac{10}{\sqrt{2}}\approx7.07

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