SOLUTION: You deposit $400 each month into an account earning 3% interest compounded monthly.
a) How much will you have in the account in 30 years?
b) How much total money will you put int
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Question 1191377: You deposit $400 each month into an account earning 3% interest compounded monthly.
a) How much will you have in the account in 30 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to calculate the future value, total deposits, and total interest earned:
**a) Future Value:**
We'll use the future value of an ordinary annuity formula:
FV = P * [((1 + r)^n - 1) / r]
Where:
* FV = Future Value (what we want to find)
* P = Periodic Payment ($400)
* r = Interest rate per period (3% per year / 12 months = 0.03/12 = 0.0025)
* n = Number of periods (30 years * 12 months/year = 360 months)
FV = 400 * [((1 + 0.0025)^360 - 1) / 0.0025]
FV = 400 * [(2.4573 - 1) / 0.0025]
FV = 400 * [1.4573 / 0.0025]
FV = 400 * 582.92
FV ≈ $233,168
**b) Total Deposits:**
Total Deposits = Monthly Deposit * Number of Months
Total Deposits = $400 * 360
Total Deposits = $144,000
**c) Total Interest Earned:**
Total Interest Earned = Future Value - Total Deposits
Total Interest Earned = $233,168 - $144,000
Total Interest Earned ≈ $89,168
**Summary:**
* **a) Future Value:** Approximately $233,168
* **b) Total Deposits:** $144,000
* **c) Total Interest Earned:** Approximately $89,168
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
The correct answer to (a) is = $233,094.75.
The correct answer to (c) is $233,094.75 - $144,000 = $89,094.75.
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