Answer:
The formula for the present value (\(PV\)) of a future sum with continuous compounding is given by:
\[ PV = \frac{FV}{e^{rt}} \]
where:
- \(FV\) is the future value,
- \(r\) is the annual interest rate (as a decimal),
- \(t\) is the time in years,
- \(e\) is the mathematical constant approximately equal to 2.71828.
In this case:
- \(FV = $6000\),
- \(r = 0.02\) (2% as a decimal),
- \(t = 9\) years.
Substitute these values into the formula to calculate the present value (\(PV\)).
Explanation:
The present value (\(PV\)) of a bond that will mature to $6000 in nine years with a 2% annual interest rate compounded continuously is approximately $4912.88. Charmaine should pay around $4912.88 for the bond now.