Question 1173174: A local university is planning to invest $500,000 every 3 months in an investment which earns interest at the rate of 12% per year compounded quarterly. The first investment will be at the end of this current quarter. a) To what sum will be the investment grow at the end of 5 years. b) How much interest will be earned during this period?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this investment problem step-by-step:
**a) To what sum will the investment grow at the end of 5 years?**
1. **Identify the variables:**
* Payment (PMT): $500,000
* Interest rate per year (r): 12% or 0.12
* Compounding frequency (n): Quarterly, so 4 times per year
* Interest rate per period (i): r/n = 0.12 / 4 = 0.03
* Number of years (t): 5
* Total number of periods (N): t * n = 5 * 4 = 20
2. **Use the future value of an ordinary annuity formula:**
* FV = PMT * [((1 + i)^N - 1) / i]
3. **Plug in the values:**
* FV = $500,000 * [((1 + 0.03)^20 - 1) / 0.03]
* FV = $500,000 * [((1.03)^20 - 1) / 0.03]
* FV = $500,000 * [(1.80611123467 - 1) / 0.03]
* FV = $500,000 * [0.80611123467 / 0.03]
* FV = $500,000 * 26.870374489
* FV = $13,435,187.24 (approximately)
Therefore, the investment will grow to approximately $13,435,187.24 at the end of 5 years.
**b) How much interest will be earned during this period?**
1. **Calculate the total amount invested:**
* Total investment = PMT * N = $500,000 * 20 = $10,000,000
2. **Calculate the total interest earned:**
* Total interest = FV - Total investment
* Total interest = $13,435,187.24 - $10,000,000
* Total interest = $3,435,187.24
Therefore, the total interest earned during this period will be approximately $3,435,187.24.
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