Question

Use the compound interest formulas P = B(1+r/k)⁻ᵏᵀ for present value p=Be⁻ʳᵀ. Find the present value of $31,000 over a term of 7 years at an annual interest rate of 5% if interest is compounded continuously.

Answer 1

Explanation:

To find the present value (P) of $31,000 over 7 years at an annual interest rate of 5% compounded continuously, use the formula P = Be^(-rT).

P is the present value.

B is the future value or initial amount, which is $31,000.

r is the annual interest rate (5% or 0.05 as a decimal).

T is the time period, which is 7 years.

P = 31,000 * e^(-0.05 * 7)

P ≈ $21,676.09 (rounded to two decimal places)

The present value is approximately $21,676.09