How much would you need to deposit in an account each month in order to have $20,000 in the account in 6 years? Assume the account earns 2% interest.

Answer 1

"""

For this problem, we will be using the Future

Value of an Annuity Formula:

FV = M * ((1+r)^n - 1) / r)

where

FV = Future value ($),

M = Periodic payment ($),

r = interest rate per period, and

n = number of periods.

From the problem, we know that FV = $20,000,

the annual interest rate is 0.02, and the total time

is 6 years. The problem asks for the amount of the

monthly payment, so we solve for 'M' in the expression

above:

M = (FV * r) / ((1+r)^n - 1)).

"""

# Given data from the problem

future_value = 20000 # future value needed for retirement ($)

annual_interest_rate = 0.02 # annual interest rate

years = 6 # number of years until retirement

# Convert annual interest rate to monthly and calculate the number of months

monthly_interest_rate = annual_interest_rate / 12

total_months = years * 12

# Calculate the monthly deposit needed (M) using the annuity formula

monthly_deposit = (future_value * monthly_interest_rate) / ((1 + monthly_interest_rate)**total_months - 1)

# Calculate total amount deposited and interest earned

total_deposited = monthly_deposit * total_months

# Output the results

print(f"Monthly deposit needed: ${monthly_deposit:.2f}")

"""

The following output should print upon runnin this code:

Monthly deposit needed: $261.68

""";