Question 1173154
Let's break down each scenario and calculate the future value of the deposits:

**(a) Annual Deposits of $10,000**

* **Deposit (PMT):** $10,000
* **Interest Rate (r):** 10% or 0.10
* **Number of Years (n):** 6
* **Compounding:** Annually

We'll use the future value of an ordinary annuity formula:

FV = PMT * [((1 + r)^n - 1) / r]

FV = $10,000 * [((1 + 0.10)^6 - 1) / 0.10]
FV = $10,000 * [(1.10^6 - 1) / 0.10]
FV = $10,000 * [(1.771561 - 1) / 0.10]
FV = $10,000 * [0.771561 / 0.10]
FV = $10,000 * 7.71561
FV = $77,156.10

**(b) Semi-annual Deposits of $5,000**

* **Deposit (PMT):** $5,000
* **Annual Interest Rate (r):** 10% or 0.10
* **Semi-annual Interest Rate (i):** 0.10 / 2 = 0.05
* **Number of Years (n):** 6
* **Number of Periods (N):** 6 * 2 = 12
* **Compounding:** Semi-annually

FV = PMT * [((1 + i)^N - 1) / i]

FV = $5,000 * [((1 + 0.05)^12 - 1) / 0.05]
FV = $5,000 * [(1.05^12 - 1) / 0.05]
FV = $5,000 * [(1.795856 - 1) / 0.05]
FV = $5,000 * [0.795856 / 0.05]
FV = $5,000 * 15.917127
FV = $79,585.64

**(c) Quarterly Deposits of $2,500**

* **Deposit (PMT):** $2,500
* **Annual Interest Rate (r):** 10% or 0.10
* **Quarterly Interest Rate (i):** 0.10 / 4 = 0.025
* **Number of Years (n):** 6
* **Number of Periods (N):** 6 * 4 = 24
* **Compounding:** Quarterly

FV = PMT * [((1 + i)^N - 1) / i]

FV = $2,500 * [((1 + 0.025)^24 - 1) / 0.025]
FV = $2,500 * [(1.025^24 - 1) / 0.025]
FV = $2,500 * [(1.808734 - 1) / 0.025]
FV = $2,500 * [0.808734 / 0.025]
FV = $2,500 * 32.34936
FV = $80,873.40

**Summary**

* **(a)** $77,156.10
* **(b)** $79,585.64
* **(c)** $80,873.40