Question

To find out how much Kay Den needs to invest for the value of the account to reach a certain amount when compounded continuously, you can use the formula for continuous compounding:

A=P⋅eʳᵗ
Where:
A is the future value of the investment.
P is the principal amount (the initial investment).
r is the annual interest rate (as a decimal).
t is the time the money is invested for (in years).
ee is the base of the natural logarithm, approximately equal to 2.71828.
In this case, Kay Den wants to determine the initial investment (P), and we know:
A is the desired future value.
r is 4.2% or 0.042 as a decimal.

Answer 1

Kay Den can find the initial investment (P) required for an account to reach a specified future value by rearranging the continuous compounding formula: P = A / (e^rt). The annual interest rate is 4.2% (r = 0.042), and with the time (t) invested, these values are substituted into the equation.

Step-by-step explanation:

To determine Kay Den's initial investment (P) needed for the account to reach a certain future value when compounded continuously, we use the formula for continuous compounding:

A = P · ert

Where:

• A is the future value of the investment.
• P is the principal amount (the initial investment).
• r is the annual interest rate (as a decimal).
• t is the time the money is invested for (in years).
• e is the base of the natural logarithm, approximately equal to 2.71828.

In this scenario, compound interest can be calculated by taking the difference between the future value and the initial investment.

To solve for P, you rearrange the initial formula:

P = A / ert

You are given the future value (A) and the annual interest rate (r = 0.042 or 4.2%). You would need to know the time (t) the money is invested for and plug these values into the equation to find the initial investment amount.