1. You need $200,000 to retire in 10 years. You can invest monthly amounts at 5% APR at work. How much should you contribute each month?

2. A friend creates an IRA with an APR of 6.25%. She starts at age 25 and deposits $50 per month.
a) How much will her IRA contain when she retires at age 65?
b) What is the total amount of her deposits?

Can someone please help me with these 2 questions and explain the steps.

Thanks!

Sure! I can help you with these questions and explain the steps involved. Let's break it down:

Question 1: You need $200,000 to retire in 10 years. You can invest monthly amounts at 5% APR at work. How much should you contribute each month?

To calculate the monthly contribution needed, we can use the formula for future value of a series of regular deposits.

Step 1: Convert the annual interest rate to a monthly rate. Since the APR is 5%, the monthly interest rate would be 5% divided by 12 (number of months in a year), which is approximately 0.4167%.

Step 2: Calculate the number of months. You want to retire in 10 years, which is 10 years times 12 months, giving us a total of 120 months.

Step 3: Calculate the future value of the monthly contributions using the formula:

Future Value = Monthly Deposit * [(1 + Monthly Interest Rate)^(Number of Months) - 1] / Monthly Interest Rate

Let's plug in the numbers:

Future Value = Monthly Deposit * [(1 + 0.004167)^(120) - 1] / 0.004167

We want the Future Value to be $200,000, so we can rearrange the equation to solve for the Monthly Deposit:

Monthly Deposit = [Future Value * Monthly Interest Rate] / [(1 + Monthly Interest Rate)^(Number of Months) - 1]

Substituting the values:

Monthly Deposit = [$200,000 * 0.004167] / [(1 + 0.004167)^(120) - 1]

By plugging in these values into the equation and solving, you should get the amount you need to contribute each month to reach your retirement goal.

Question 2:

a) How much will her IRA contain when she retires at age 65?

To calculate the future value of her IRA when she retires at age 65, we can use the formula for future value of a series of regular deposits.

Step 1: Convert the annual interest rate to a monthly rate. Since the APR is 6.25%, the monthly interest rate would be 6.25% divided by 12 (number of months in a year), which is approximately 0.5208%.

Step 2: Calculate the number of months. She starts at age 25 and retires at age 65, which is a total of 40 years. Multiply that by 12 months to get a total of 480 months.

Step 3: Calculate the future value of the monthly deposits using the formula:

Future Value = Monthly Deposit * [(1 + Monthly Interest Rate)^(Number of Months) - 1] / Monthly Interest Rate

Let's plug in the numbers:

Future Value = $50 * [(1 + 0.005208)^(480) - 1] / 0.005208

By solving this equation, you should get the total value of her IRA when she retires at age 65.

b) What is the total amount of her deposits?

To calculate the total amount of her deposits, you can simply multiply the monthly deposit amount by the total number of months.

Total Deposits = Monthly Deposit * Number of Months

Substituting the values:

Total Deposits = $50 * 480

By multiplying these numbers, you will get the total amount of her deposits.

I hope this helps! Let me know if you have any further questions.