Math Problem Statement
The present value of FV dollars compounded at an interest rate i per period for n periods is PV=FV/(1+i)^n. In the formula, PV represents the present value, FV is the future value after n compounding periods. When the annual interest i is compounded m times per year, the interest rate per period is understood to be i/m. Find the present value of the given future amount of $10,752.34 at 3.3% compounded annually for 5 years.(Do not round until the final answer. Then round to the nearest cent as needed.)
Solution
To solve this problem, we will use the present value formula:
where:
- (the future value),
- (3.3% annual interest rate),
- years (since it's compounded annually, is 5).
Now, let's plug in the values into the formula:
Step-by-step calculation:
- Calculate .
- Raise 1.033 to the power of 5:
- Divide the future value by this result:
So, the present value is approximately $9,149.41.
Would you like further details or have any questions?
Here are 5 related questions you might find helpful:
- How does the compounding frequency affect the present value calculation?
- What would be the present value if the interest rate increased to 5%?
- How do we calculate present value for continuous compounding?
- What happens to the present value if the future value increases?
- How does the time period (n) impact the present value?
Tip: The more frequent the compounding, the lower the present value will be for the same future amount.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Present Value Calculation
Exponential Growth
Formulas
PV = FV / (1 + i)^n
Theorems
Compound Interest Formula
Suitable Grade Level
Grades 11-12
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