You invest Php1,500 in a bank account that offers an annual interest rate of 3.5%, compounded quarterly. What will your balance be after 3 years?

Sure, here's how you can calculate it:

1. First, you need to understand the formula for compound interest, which is A = P (1 + r/n)^(nt). In this formula:

   • A is the amount of money accumulated after n years, including interest.
   • P is the principal amount (the initial amount of money).
   • r is the annual interest rate (in decimal).
   • n is the number of times that interest is compounded per year.
   • t is the time the money is invested for in years.

2. Now, plug in the given values into the formula. In this case:

   • P = Php1,500
   • r = 3.5/100 = 0.035 (you divide by 100 to convert the percentage into a decimal)
   • n = 4 (since the interest is compounded quarterly)
   • t = 3

3. Substituting these values into the formula gives you A = 1500 (1 + 0.035/4)^(4*3).

4. Simplify the equation inside the parentheses to get A = 1500 (1 + 0.00875)^(12).

5. Further simplifying gives you A = 1500 * 1.00875^(12).

6. Calculating 1.00875^(12) gives you approximately 1.1086.

7. Finally, multiply this by the initial amount to get A = 1500 * 1.1086 = Php1,662.90.

So, after 3 years, your balance will be approximately Php1,662.90.