We will use the future value of an ordinary annuity formula to approximate the interest rate:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

where:

• $FV = 5881.83$ (future value),
• $P = 1000$ (annual payment),
• $n = 5$ years,
• $r$ is the annual interest rate (which we need to find).

Step 1: Set Up the Equation

$5881.83 = 1000 \times \frac{(1 + r)^5 - 1}{r}$

Step 2: Solve for $r$

This equation does not have a straightforward algebraic solution, so we will approximate $r$ using numerical methods. I'll compute it now. scipy.optimize import fsolve

Given values

FV = 5881.83 # Future value P = 1000 # Annual payment n = 5 # Number of years

Define the equation to solve for r

def annuity_equation(r): return P * ((1 + r)**n - 1) / r - FV

Initial guess for the interest rate

r_guess = 0.05 # 5%

Solve for r

r_solution = fsolve(annuity_equation, r_guess)[0]

Convert to percentage

r_percentage = r_solution * 100 r_percentageThe approximate annual nominal compounding interest rate is 8.13%.

Would you like a breakdown of the numerical solving process or any additional explanations?

Here are some related questions to explore:

1. How does the future value of an annuity change with different interest rates?
2. What is the difference between an ordinary annuity and an annuity due?
3. How can graphical approximation methods be used to estimate interest rates?
4. What happens if payments are made semi-annually instead of annually?
5. How does increasing the number of years affect the accumulated amount?

Tip: If you want to solve annuity problems efficiently, learning how to use financial calculators or Excel functions (like FV or RATE) can be very helpful!