karissa’s house went from a valuation of 12 million php (philippine peso) on 1st january 2007, to 8 million php on 1st january 2012. if the value of the house compounded monthly, what was the annual rate of change? give your answer in percentage, correct to 1 decimal place.

Sagot :

By using compound interest, it is found that the annual rate of increase was of 0.132%.

Given,

Valuation of 12 million php on 1st January 2007

8 million php on 1st January 2012.

Annual rate of change - ?

The amount of money earned, in compound interest after t years, is given as follows:

[tex]A(t) = P (1 +\frac{r}{n}) ^{nt}[/tex]

For this problem, the parameters are:

t = 5,  A(t) = 6,  A(0) = 12,  n = 12.

Here,

P is the principal which is the initial sum of money.

A(t) is considered the amount of money after t years.

n is the number of times where interest is compounded.

r is the interest rate.

Thus, we solve for r to find the interest rate as follows:

[tex]A(t) = P (1 + \frac{r}{n}) ^{nt}[/tex]

[tex]8 = 12 (1 + \frac{r}{12}) ^{12X5}[/tex]

[tex](1 + \frac{r}{12})^{60} = 0.66[/tex]

[tex]\sqrt[60]{1 + \frac{r}{12}} ^{60}[/tex]   = [tex]\sqrt[60]{0.66}[/tex]

[tex]1 + \frac{r}{12} = (0.66)^{\frac{1}{60}}[/tex]

1 + r/12 = 1.011

r/12 = 0.011

r = 12 x 0.011

r = 0.132

Hence, the annual rate of increase is of 0.132%.

To learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ4