Math Problem Statement
Suppose you deposit $8800 into a savings account that earns 8.88% interest, compounded monthly.
Fill in the following table, rounding to the nearest cent.
Month Interest Amount Balance 1 $ $ 2 $ $ 3 $ $ 4 $ $
Solution
We can solve this problem using the compound interest formula:
Where:
- is the amount of money in the account after years (final balance).
- is the principal amount (initial deposit) = $8800.
- is the annual interest rate = 8.88% = 0.0888.
- is the number of times the interest is compounded per year = 12 (monthly compounding).
- is the time in years.
For each month, the formula for the new balance is: The interest earned in each month is the difference between the new and old balances:
Step-by-step calculation:
Month 1: Interest earned in Month 1:
Month 2: Interest earned in Month 2:
Month 3: Interest earned in Month 3:
Month 4: Interest earned in Month 4:
Filled Table:
Month | Interest Amount | Balance |
---|---|---|
1 | $65.12 | $8865.12 |
2 | $65.78 | $8930.90 |
3 | $66.46 | $8997.36 |
4 | $67.16 | $9064.52 |
Would you like any further details, or have any questions?
5 Related Questions:
- What happens to the balance if the interest rate changes to 10%?
- How is the balance affected if compounding is done quarterly instead of monthly?
- What is the formula for continuous compounding, and how would the balance change if used?
- How does the time period affect the amount of interest earned?
- How would different initial deposit amounts change the outcomes?
Tip: The more frequent the compounding periods, the faster your balance grows due to the effect of interest on interest!
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Exponential Growth
Formulas
Compound interest formula: A = P(1 + r/n)^(nt)
Monthly interest formula: A_new = A_old(1 + r/n)
Interest earned formula: Interest = A_new - A_old
Theorems
-
Suitable Grade Level
Grades 9-12
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