Final answer:
To calculate the future values of annuities, the future value formula for ordinary annuities is used, with specifics of periodic payments, interest rate, and number of payments being inserted for each scenario.
Step-by-step explanation:
To find the future value of an annuity, you need to use the future value formula for an ordinary annuity:
FV = P × [((1 + r)n - 1) / r]
Where:
- FV is the future value of the annuity.
- P is the periodic payment amount.
- r is the periodic interest rate (annual interest rate divided by the number of compounding periods per year).
- n is the total number of payments (compounding periods per year multiplied by the number of years).
For the monthly payments of Php 5,000.00:
P = 5000
r = 3% per annum / 12 months = 0.0025 per month
n = 5 years × 12 months/year = 60 payments
Insert these values into the formula to get the future value for annuity a.
For the quarterly payments of Php 3,000:
P = 3000
r = 2% per annum / 4 quarters = 0.005 per quarter
n = 6 years × 4 quarters/year = 24 payments
Repeat the process with these values to get the future value for annuity b.