Question

After graduating from college you have your first job in your area of study and are making $115,000 per year.

You are paid once each month and decide to put 10% of each paycheck into your retirement account at the end of each month.
How much will you deposit into the accounteach month? Round to the nearest $1.


$ per month

For the parts below, use the rounded value for your deposit amount.

The investements that you chosen to invest in average 7% growth per year compounded monthly.
How much will you expect to have in the account in 30 years?


$

How much total money will you put into the account?


$

How much total growth/interest should you expect will you earn?


$

If you manage to save an additional $100 each month, how much will you have in the account after 30 years?


$

Answer 1

The individual will deposit $958 into the retirement account each month, which will grow to approximately $2,625,858 after 30 years due to compound interest. The total contribution will be $344,880, and the total growth will be around $2,280,978. With the additional $100 monthly saving, the total would increase to approximately $2,900,396 after 30 years.

Step-by-step explanation:

To calculate the monthly retirement contribution, we take 10% of the annual salary of $115,000 and divide by 12 (the number of months in a year).

Monthly deposit = ($115,000 * 0.10) / 12 = $11,500 / 12 = $958.33

Rounded to the nearest dollar, the monthly deposit is $958 per month.

Now, let's calculate the future value of the retirement account after 30 years using the compound interest formula:

FV = P * ((1 + r/n)^(nt))

Where:

FV = future value of the investment

P = principal amount (monthly deposit)

r = annual interest rate (expressed as a decimal)

n = number of times the interest is compounded per year

t = number of years

We assume monthly compounding (n = 12) and an annual interest rate of 7% (r = 0.07):

FV = $958 * ((1 + 0.07/12)^(12*30))

FV ≈ $958 * ((1 + 0.00583)^360)

FV ≈ $958 * (1.00583^360)

FV ≈ $958 * 7.6123

FV ≈ $7294.05 per month

Total contributed over 30 years: $958 * 12 * 30 = $344,880

Total expected in the account after 30 years: $7294.05 * 12 * 30 = $2,625,858

Total growth/interest earned: $2,625,858 - $344,880 = $2,280,978

If an additional $100 is saved each month, the new monthly deposit is $958 + $100 = $1,058.

With the new monthly deposit:

FV = $1,058 * ((1 + 0.07/12)^(12*30))

FV ≈ $1,058 * 7.6123

FV ≈ $8056.83 per month

Total expected in the account after 30 years with the additional savings: $8056.83 * 12 * 30 = $2,900,396

Answer 2

$11,500 per year or $958.33 per monthThe amount of money you will have in your account in 30 years would be $1,311,715.94The total money you will put into the account is $3,465,000The total growth/interest you should expect to earn is $946,315.94If you manage to save an additional $100 each month, you will have $1,385,719.71 in the account after 30 years.

Step-by-step explanation: