I'll go through each question one at a time and provide solutions. Let's start with Question 1.

1. Solution for Question 1

Question 1:

Suppose Mr. and Mrs. Mariano deposit ₱20,000.00 at the end of each year for 5 years in an investment account that earns 10% per year compounded annually. What is the amount of this annuity?

This is a future value of an ordinary annuity problem, where payments are made at the end of each period.

Formula:

The future value of an ordinary annuity (FV) is given by: $FV = P \times \frac{(1 + r)^n - 1}{r}$ where:

• $P = 20,000$ (annual deposit)
• $r = 0.10$ (interest rate per period, compounded annually)
• $n = 5$ (number of years)

Solution:

$FV = 20,000 \times \frac{(1 + 0.10)^5 - 1}{0.10}$ Calculating each part:

1. $(1 + 0.10)^5 = 1.10^5 \approx 1.61051$
2. $1.61051 - 1 = 0.61051$
3. $\frac{0.61051}{0.10} = 6.1051$
4. $20,000 \times 6.1051 = 122,102$

Future Value (Amount of the annuity) = ₱122,102

Next Steps

Would you like me to continue with the other questions, or do you need more details for this one?

Additional Questions to Consider:

1. What if the deposit period was 10 years instead of 5 years?
2. How would the final amount change if the interest rate was 8% instead of 10%?
3. How would the formula adjust if payments were made at the beginning of each period (annuity due)?
4. What would happen if compounding was quarterly instead of annually?
5. How much would Mr. and Mrs. Mariano earn if they stopped depositing after 3 years?

Tip: For annuity problems, always check if the payment is at the beginning or end of the period, as this affects the type of annuity formula you use.