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PYTHON CODE ONLY!
Assume:
1. Your semiannual raise is .07 (7%)
2. Your investments have an annual return of 0.04 (4%)
3. The down payment is 0.25 (25%) of the cost of the house
4. The cost of the house that you are saving for is $1M.
You are now going to try to find the best rate of savings to achieve a down payment on a $1M house in 36 months. Since hitting this exactly is a challenge, we simply want your savings to be within $100 of the required down payment.
Write a program to calculate the best savings rate, as a function of your starting salary. You should use bisection search to help you do this efficiently. You should keep track of the number of steps it takes your bisections search to finish.
Expert Answer
main.py
def find_best_savings_rate(starting_salary):
low = 0
high = 10000
steps = 0
# Bisection search for the best savings rate
while True:
steps += 1
best_savings_rate_guess = (high + low) // 2
current_savings = 0
annual_salary = starting_salary
for months in range(36):
current_savings += annual_salary / 12 * best_savings_rate_guess / 10000 + current_savings * 0.04 / 12
# Salary is raised for 7% AFTER every 6 months
if months != 0 and months % 6 == 0:
annual_salary += annual_salary * 0.07
# Savings + or - 100$ are OK
if 249900 <= current_savings <= 250100:
print("Best savings rate:", best_savings_rate_guess / 10000)
print("Steps in bisection search:", steps)
return
if current_savings < 249900:
low = best_savings_rate_guess
elif current_savings > 250100:
high = best_savings_rate_guess
if steps > 14:
print("It is not possible to pay the down payment in three years.")
return
salary = int(input("Enter the starting salary:"))
find_best_savings_rate(salary)
output:
