Math Problem Statement
An account earns an annual rate of 6.9% compounded weekly. If $1,000 is deposited into this account, then after 5 years there is $____.
Round your answer to two decimal places.
Solution
To calculate the amount of money in the account after 5 years with an annual interest rate of 6.9% compounded weekly, we use the compound interest formula:
Where:
- is the future value of the investment.
- is the principal amount.
- is the annual interest rate (expressed as a decimal).
- is the number of compounding periods per year (weekly compounding).
- is the time in years.
Plugging in the values:
Let me compute this.# Defining the variables P = 1000 # Principal amount r = 0.069 # Annual interest rate n = 52 # Compounding periods per year (weekly) t = 5 # Time in years
Compound interest formula
A = P * (1 + r / n) ** (n * t) A_rounded = round(A, 2) A_rounded1411.671411.67successAfter 5 years, the account will have $1,411.67.
Would you like further details on the calculations, or do you have any additional questions? Here are 5 related questions to explore further:
- How would the total change if the interest rate were compounded monthly instead of weekly?
- What would be the total if the initial deposit was $2,000 instead of $1,000?
- How does the final amount compare if the time is extended to 10 years instead of 5?
- What is the effective annual rate (EAR) for this account with weekly compounding?
- Can we compute the amount if additional deposits are made annually?
Tip: Compounding more frequently (e.g., weekly vs. annually) increases the final amount, but the differences become less significant at very high compounding frequencies.
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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
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