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The other question is in the picture

Activity 2: of Directions: Write T before each item if the statement is TRUE, otherwise write F.

For items 1-2: Use the problem below to answer the following questions.

Your mother invested PhP 10,000.00 in an investment institution at 5% compounded semi-annually for x years.

___1. y = 10 000(1.025)2x is the function that represents mother's total investment​

The other question is in the picture Activity 2 of Directions Write T before each item if the statement is TRUE otherwise write F For items 12 Use the problem b class=

Respuesta :

Using compound interest, it is found that the correct options are:

1. True.

2. True.

Compound interest:

[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]

  • A(t) is the amount of money after t years.  
  • P is the principal(the initial sum of money).  
  • r is the interest rate(as a decimal value).  
  • n is the number of times that interest is compounded per year.  
  • x is the time in years for which the money is invested or borrowed.

Item 1:

  • Invested 10000, hence [tex]P = 10000[/tex].
  • Semi-annually, hence [tex]n = 2[/tex].
  • Interest rate of 5%, hence [tex]r = 0.05[/tex]

Then:

[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]

[tex]A(x) = 10000\left(1 + \frac{0.05}{2}\right)^{2x}[/tex]

[tex]A(x) = 10000(1.025)^{2x}[/tex]

Hence option 1 is True.

Item 2:

  • Quarterly, hence [tex]n = 4[/tex].

Then:

[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]

[tex]A(x) = 10000\left(1 + \frac{0.05}{4}\right)^{4x}[/tex]

[tex]A(x) = 10000(1.0125)^{4x}[/tex]

Hence option 2 is also True.

A similar problem is given at https://brainly.com/question/24507395