Question

Math pls patulong

Answer 1

Using compound interest, it is found that:

• With interest compound quarterly, the balance is of Php 5,804.

• With interest compound annually, the balance is of Php 5,796.

• Due to the higher balance, the quarterly compound gives the higher interest.

Compound interest:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

• 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.  

• t is the time in years for which the money is invested or borrowed.

In this problem:

• Rate of 3%, hence $r = 0.03$.

• Compounded quarterly, hence $n = 4$.

• Initial deposit of 50000, hence $P = 50000$.

• Five years, hence $t = 5$.

Then, the balance is:

$A(5) = P\left(1 + \frac{r}{n}\right)^{nt}$

$A(5) = 5000\left(1 + \frac{0.03}{4}\right)^{4(5)}$

$A(5) = 5804$

With interest compound quarterly, the balance is of Php 5,804.

Now, with annual interest, we have that $n = 1$, and:

$A(5) = P\left(1 + \frac{r}{n}\right)^{nt}$

$A(5) = 5000\left(1 + \frac{0.03}{1}\right)^{1(5)}$

$A(5) = 5796$

With interest compound annually, the balance is of Php 5,796.

Due to the higher balance, the quarterly compound gives the higher interest.

To learn more about compound interest, you can take a look at brainly.com/question/25781328