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Math pls patulong

You are a bank financier. Your bank pays an annual interest rate of 3% compounded
quarterly. If the initial deposit (or principal), of your client is Php 50 000, find the
balance after 5 years.

You have to show the balance of Php 50 000 after 5 years if the bank pays an interest
rate of 3% compounded annually. Which gives a higher interest between the two?
Explain.

Math Pls Patulong You Are A Bank Financier Your Bank Pays An Annual Interest Rate Of 3 Compounded Quarterly If The Initial Deposit Or Principal Of Your Client I class=

Sagot :

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:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/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.  
  • t is the time in years for which the money is invested or borrowed.

In this problem:

  • Rate of 3%, hence [tex]r = 0.03[/tex].
  • Compounded quarterly, hence [tex]n = 4[/tex].
  • Initial deposit of 50000, hence [tex]P = 50000[/tex].
  • Five years, hence [tex]t = 5[/tex].

Then, the balance is:

[tex]A(5) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(5) = 5000\left(1 + \frac{0.03}{4}\right)^{4(5)}[/tex]

[tex]A(5) = 5804[/tex]

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

Now, with annual interest, we have that [tex]n = 1[/tex], and:

[tex]A(5) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(5) = 5000\left(1 + \frac{0.03}{1}\right)^{1(5)}[/tex]

[tex]A(5) = 5796[/tex]

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 https://brainly.com/question/25781328

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