To complete the table, we need to calculate the value resulting from the $14,000 investment with a 4% interest rate for 5 years under the given compounding options.
a. Daily compounding:
To calculate the value with daily compounding, we use the formula:
Value = Principal × (1 + (Rate / n))^(n × Time)
In this case, the principal (P) is $14,000, the rate (R) is 4% (or 0.04), the time (T) is 5 years, and the compounding period (n) is 365 (since it's daily compounding).
Value = 14000 × (1 + (0.04 / 365))^(365 × 5)
Calculating this value will give you the result for the daily compounding option.
b. Continuously compounding:
To calculate the value with continuous compounding, we use the formula:
Value = Principal × e^(Rate × Time)
In this case, the principal (P) is $14,000, the rate (R) is 4% (or 0.04), and the time (T) is 5 years.
Value = 14000 × e^(0.04 × 5)
Calculating this value will give you the result for the continuously compounding option.
Please note that e represents the mathematical constant approximately equal to 2.71828.