Question 1191374: Suppose you want to have $800,000 for retirement in 30 years. Your account earns 10% interest
a) How much would you need to deposit in the account each month?
b) How much interest will you earn?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the monthly deposit and the total interest earned:
**a) Calculating the Monthly Deposit:**
We'll use the future value of an ordinary annuity formula, which is:
FV = P * [((1 + r)^n - 1) / r]
Where:
* FV = Future Value ($800,000)
* P = Periodic Payment (what we want to find)
* r = Interest rate per period (10% per year, so 10%/12 per month, or 0.1/12)
* n = Number of periods (30 years * 12 months/year = 360 months)
Let's rearrange the formula to solve for P:
P = FV * [r / ((1 + r)^n - 1)]
Now, plug in the values:
P = $800,000 * [(0.1/12) / ((1 + 0.1/12)^360 - 1)]
P = $800,000 * [0.008333 / (1.008333^360 - 1)]
P = $800,000 * [0.008333 / (19.788 - 1)]
P = $800,000 * [0.008333 / 18.788]
P ≈ $353.91
So, you would need to deposit approximately $353.91 each month.
**b) Calculating the Total Interest Earned:**
1. **Calculate the total amount deposited:**
Total Deposited = Monthly Deposit * Number of Months
Total Deposited = $353.91 * 360
Total Deposited ≈ $127,407.60
2. **Calculate the total interest earned:**
Total Interest Earned = Future Value - Total Deposited
Total Interest Earned = $800,000 - $127,407.60
Total Interest Earned ≈ $672,592.40
Therefore, you will earn approximately $672,592.40 in interest.
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