You deposit $300 each month into an account earning 8% interest compounded monthly.

a) How much will you have in the account in 35 years?

b) How much total money will you put into the account?

c) How much total interest will you earn?

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To calculate the values, we can use the formula for compound interest:

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

where:

A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

a) To calculate how much you will have in the account in 35 years, we can use the formula:

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

A = 300(1 + 0.08/12)^(12*35)

Calculating this, we find:

A ≈ $459,426.64

So you will have approximately $459,426.64 in the account in 35 years.

b) To determine the total money you will put into the account, we need to calculate the total amount invested over 35 years. Since you deposit $300 each month, the total number of deposits would be:

35 years * 12 months/year = 420 deposits

The total money you will put into the account can be calculated as:

Total Money Invested = Monthly Deposit * Total Deposits

Total Money Invested = $300 * 420

Total Money Invested = $126,000

Therefore, you will put a total of $126,000 into the account over 35 years.

c) To find the total interest you will earn, we can subtract the principal amount from the total amount in the account after 35 years. The total interest is the difference between these two amounts:

Total Interest = Total Amount - Principal Amount

Total Interest = $459,426.64 - $126,000

Total Interest ≈ $333,426.64

Thus, you will earn approximately $333,426.64 in interest over 35 years.

To find out how much you will have in the account in 35 years, you can use the formula for compound interest:

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

Where:
A = the future value of the account (what you will have in the account)
P = the initial deposit (in this case, $300)
r = the annual interest rate (in this case, 8% or 0.08)
n = the number of times the interest is compounded per year (in this case, monthly, so 12)
t = the number of years (in this case, 35)

a) Plugging the values into the formula, we get:

A = 300(1 + 0.08/12)^(12*35)
A = 300(1 + 0.0067)^(420)
A ≈ $3,505.07

Therefore, you will have approximately $3,505.07 in the account after 35 years.

b) To find out how much total money you will put into the account, you can multiply the monthly deposit amount by the number of months (35 years * 12 months/year):

Total deposits = $300 * 12 * 35
Total deposits = $126,000

Therefore, the total amount of money you will put into the account is $126,000.

c) To calculate the total interest earned, you can subtract the total deposits from the future value of the account:

Total interest = future value - total deposits
Total interest = $3,505.07 - $126,000
Total interest = -$122,494.93

However, the negative sign indicates that you have lost money rather than earning interest. This could be due to calculations, but it is essentially because the interest rate (8%) is less than the inflation rate over the 35-year period.