Math Problem Statement
Solution
To solve this problem, we use the formula for continuous compounding:
Where:
- is the future amount ($7,000 in this case),
- is the present amount (the amount Jerome should ask for),
- is the annual interest rate (4% = 0.04),
- is the time in years (2 years),
- is the mathematical constant approximately equal to 2.718.
We solve for :
Substituting the values:
Let me calculate this for you:
So, Jerome should ask for $6,463.97.
Let me know if you'd like a breakdown or have further questions!
5 Related Questions:
- How would the amount change if the interest rate were 5% instead of 4%?
- What happens to the amount needed if the time period changes to 3 years?
- How would the result differ if the interest were compounded annually instead of continuously?
- What formula would you use for simple interest instead of continuous compounding?
- What if Jerome wanted to save for a $10,000 car instead? How much would he need now?
Tip:
When working with continuous compounding, remember that small changes in the rate or time can have a significant effect due to exponential growth.
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Math Problem Analysis
Mathematical Concepts
Continuous Compounding
Exponential Growth
Algebra
Formulas
A = P * e^(rt)
P = A / e^(rt)
Theorems
Exponential Growth Formula
Suitable Grade Level
Grades 11-12 (Precalculus)
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