Suppose you want to have $700,000 for retirement in 30 years. Your account earns 6% interest. a) How much would you need to deposit in the account each month? b) How much interest will you earn?

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 = $700,000,

the annual interest rate is 0.06, and the total time

is 30 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)).

For part (b), we simply multiply the monthly

payment 'M' by the amount of times we made the payment,

then subtract this value from the future value, 'FV.'

"""

# Given data from the problem

future_value = 700000 # future value needed for retirement ($)

annual_interest_rate = 0.06 # annual interest rate

years = 30 # 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 (P) 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

interest_earned = future_value - total_deposited

# Output the results

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

print(f"Total interest earned over {years} years: ${interest_earned:.2f}")

"""

The following output should print upon runnin this code:

Monthly deposit needed: $696.85

Total interest earned over 30 years: $449132.68

""";