Math Problem Statement

Use the compound interest formula to find the future value A for the following values. Upper P equals $ 2 comma 500P=$2,500 i equals 0.066i=0.066 n equals 25n=25 Question content area bottom Part 1 Upper A equals $A=$enter your response here ​(Round to the nearest​ cent.)

Solution

The formula for calculating compound interest is:

A=P(1+i)nA = P(1 + i)^n

Where:

  • AA is the future value of the investment/loan, including interest.
  • PP is the principal investment amount (the initial deposit or loan amount).
  • ii is the interest rate per period.
  • nn is the number of periods.

Given:

  • P=2500P = 2500
  • i=0.066i = 0.066
  • n=25n = 25

Now, substitute these values into the formula:

A=2500(1+0.066)25A = 2500(1 + 0.066)^{25}

Let me calculate this for you.The future value AA of the investment, rounded to the nearest cent, is:

A=$12,355.78A = \$12,355.78

Would you like more details on the calculation or have any further questions?

Here are 5 related questions for further exploration:

  1. How would the future value change if the interest rate was lower, say 5%?
  2. What happens to the future value if the investment period is reduced to 20 years?
  3. How does compound interest compare to simple interest over the same time frame?
  4. What would the future value be if compounded semi-annually instead of annually?
  5. How does inflation affect the real value of the future amount?

Tip: The frequency of compounding (monthly, quarterly, etc.) can significantly impact the future value.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

A = P(1 + i)^n

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 9-12