Math Problem Statement
Solution
This is a compound interest problem where the interest is compounded semi-annually. We can use the compound interest formula to solve it:
Where:
- is the final amount.
- is the principal (initial deposit).
- (5% annual interest rate).
- because the interest is compounded semi-annually (twice a year).
- years is the time the money is left in the account.
Substituting these values into the formula:
Let's calculate:
So, the final amount after 5 years, rounded to two decimal places, is $10,112.66.
Would you like more details or have any questions?
Here are 5 related questions to explore:
- What if the interest was compounded quarterly instead of semi-annually?
- How does the final amount change if the interest rate increases to 6%?
- What if the investment period was only 3 years?
- How would the final amount change if the initial deposit was $10,000 instead of $7,900?
- What is the difference between simple interest and compound interest in terms of growth over time?
Tip: The more frequently interest is compounded, the higher the final amount will be due to the "compounding effect."
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Compound Interest
Exponential Growth
Finance Mathematics
Formulas
A = P(1 + r/n)^(nt)
Theorems
Compound Interest Theorem
Suitable Grade Level
Grades 10-12
Related Recommendation
Calculate Compound Interest: $1,100 at 2.5% for 9 Years (Semi-Annually Compounded)
Compound Interest: $2000 at 5% for 7 Years (Semi-Annual)
Calculate Compound Interest for a $5,000 Deposit with 7% Interest Compounded Monthly Over 10 Years
Compound Interest Calculation for Changing Interest Rates Over 10 Years
Calculate Annual Interest Rate for a $7,500 Investment Compounded Semi-Annually