Math Problem Statement
You deposit $300 each month into an account earning 8% interest compounded monthly. How much will be in the account in 15 years?
Solution
This is a problem involving compound interest with regular monthly deposits. The formula to calculate the future value of an annuity (regular deposits) compounded monthly is:
Where:
- = Future value of the investment/loan, including interest
- = Monthly deposit ($300 in this case)
- = Monthly interest rate (annual interest rate divided by 12)
- = Total number of payments (number of months)
Let's break down the values:
- (monthly deposit)
- Annual interest rate = 8%, so monthly interest rate
- Number of months in 15 years =
Now, we can substitute these values into the formula to find the future value.
Let's calculate this value.The amount in the account after 15 years, with monthly deposits of $300 and an 8% interest rate compounded monthly, will be approximately $103,811.47.
Would you like any further details on this calculation or have other questions?
Here are 5 related questions to expand on this concept:
- What would happen if the interest rate were 6% instead of 8%?
- How does the length of time affect the total amount accumulated in the account?
- What if you made a single lump-sum deposit instead of monthly contributions?
- How would the future value change if the interest were compounded quarterly instead of monthly?
- What if you increased the monthly deposit amount to $500?
Tip: The longer you leave money in a compound interest account, the more significant the interest becomes due to the compounding effect!
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Annuities
Time Value of Money
Formulas
Future value of annuity formula: A = P × ((1 + r)^n - 1) / r
Theorems
Compound interest theorem
Suitable Grade Level
Grades 10-12
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