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The image contains three problems, mostly related to compound interest. Let’s analyze and solve each one:

### 1. Problem 1:
A woman deposits ₦650 at the beginning of each quarter for 5 years into an account paying 8% compounded quarterly. We need to find the total value of the account at the end of 5 years.

- **Formula for future value of an annuity** (since this is a series of deposits):
\[
A = P \times \frac{(1 + r)^n - 1}{r}
\]
Where:
- \( P = 650 \, \text{(quarterly deposit)} \)
- \( r = \frac{8\%}{4} = 0.02 \, \text{(quarterly interest rate)} \)
- \( n = 4 \times 5 = 20 \, \text{(total number of quarters)} \)

### 2. Problem 2:
Ngozi’s grandfather gives her ₦1000 on each birthday from the age of 1 to 21. If the money is deposited in a bank paying 9% annual interest, what is the value of the account at age 21?

This is a problem involving a growing annuity with annual deposits. We calculate the future value of each ₦1000 deposit, compounded for different periods (since each deposit remains in the account for different durations).

The formula for each deposit is:
\[
A = P \times (1 + r)^t
\]
Where \( P = 1000 \), \( r = 0.09 \) (annual rate), and \( t \) represents the time period for each deposit.

### 3. Problem 3:
A couple plans to travel 7 years from now and deposits ₦750 every three months into an account paying 18% interest compounded quarterly. We need to calculate the total worth of the account after 7 years.

- **Formula for future value of an annuity** (similar to Problem 1):
\[
A = P \times \frac{(1 + r)^n - 1}{r}
\]
Where:
- \( P = 750 \)
- \( r = \frac{18\%}{4} = 0.045 \, \text{(quarterly interest rate)} \)
- \( n = 4 \times 7 = 28 \, \text{(total number of quarters)} \)

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I can calculate each of these for you. Which one would you like to start with, or would you like the calculations for all three problems?

1) A woman deposits ₦650 at the beginning of each quarter for 5 years into an account paying 8% compounded quarterly. What is the value of the account at the end of 5 years?
2) Ngozi's grandfather gives her ₦1000 on each birthday from the age of 1 to 21. If the money is deposited in a bank paying 9% annual interest, what is the value of Ngozi's account at age 21?
3) A couple deposits ₦750 every three months into an account paying 18% annual interest compounded quarterly for 7 years. What will be the total worth of the account at the end of 7 years?

Solve compound interest problems involving quarterly deposits, annual birthday gifts, and frequent annuity payments. Learn the formulas for calculating the future value of an annuity and single deposits with step-by-step explanations.

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