Using compound interest, it is found that a sum of $16,586.26 must be deposited.
What is compound interest?
The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
- 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:
- We want to have Php 500 to be withdrawn monthly for 5 years, hence A(t) = 500 x 12 x 5 = 30000.
- The first withdraw is 6 years from now, hence t = 6.
- The interest rate is of r = 0.09.
- Compounded quarterly, hence n = 4.
The amount deposited is the principal, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]30000 = P\left(1 + \frac{0.09}{4}\right)^{4(6)}[/tex]
[tex](1.025)^{24}P = 30000[/tex]
[tex]P = \frac{30000}{(1.025)^{24}}[/tex]
[tex]P = 16586.26[/tex]
A sum of $16,586.26 must be deposited.
To learn more about compound interest, you can take a look at https://brainly.com/question/25781328
