Math Problem Statement

Find the final amount of money in an account if is deposited at interest compounded weekly and the money is left for years.

Solution

To find the final amount of money in an account with interest compounded weekly, we can use the compound interest formula:

A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{n \cdot t}

where:

  • AA is the final amount,
  • PP is the initial principal (amount of money deposited),
  • rr is the annual interest rate (as a decimal),
  • nn is the number of compounding periods per year (for weekly compounding, n=52n = 52),
  • tt is the number of years the money is left in the account.

If you provide the specific values for the principal amount, interest rate, and number of years, I can calculate the final amount for you.

Would you like to go through an example with specific values, or do you have the numbers ready?


Related Questions

  1. What would be the final amount with monthly compounding instead of weekly?
  2. How would the final amount change if the interest was compounded daily?
  3. What would happen if the interest rate doubled?
  4. How can we calculate the amount of interest earned alone?
  5. What if the initial deposit amount changes halfway through the compounding period?

Tip: For compound interest problems, always check if the compounding frequency (e.g., weekly, monthly) aligns with the interest rate period for accurate results.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

A = P(1 + r/n)^(n * t)

Theorems

Compound Interest Formula

Suitable Grade Level

Grades 10-12