Question 1173154: A person wants to deposit $10,000 per year for 6 years. If interest is earned at the rate of
10 percent per year, compute the amount to which the deposits will grow by the end of the 6 years if:
(a) Deposits of $10,000 are made at the end of each year with interest compounded annually.
(b) Deposits of $5,000 are made at the end of each 6-month period with interest com pounded semiannually.
(e) Deposits of $2,500 are made at the end of every quarter with interest compounded
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! 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
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