Question

You deposit $400 each month into an account earning 5% interest compounded monthly. a) How much will you have in the account in 25 years? $ b) How much total money will you put into the account? $ c) How much total interest will you earn?

Answer 1

To calculate the amount of money in the account in 25 years, use the formula for compound interest. Multiply the monthly deposit by the number of months to find the total money deposited. Calculate the total interest earned by subtracting the total money deposited from the final amount.

Step-by-step explanation:

To calculate the amount of money in the account in 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A = final amount
• P = principal amount (initial deposit)
• r = annual interest rate
• n = number of times interest is compounded per year
• t = number of years

For this question, P = $400, r = 5% (0.05 in decimal form), n = 12 (compounded monthly), and t = 25:

A = 400(1 + 0.05/12)^(12 * 25)

= $1,548.27

To calculate the total money you will put into the account, multiply the monthly deposit by the number of months (25 years * 12 months):

Total Money = $400 * (25 * 12)

= $120,000

To calculate the total interest earned, subtract the total money deposited from the final amount:

Total Interest = Final Amount - Total Money

= $1,548.27 - $120,000

= -$118,451.73 (negative because the final amount is less than the total money deposited)