You deposit $300 each month into an account earning 7% interest compounded monthly.
How much will you have in the account in 15 years?
How much total money will you put into the account?
How much total interest will earn?
Here's the Link:
www.wyzant.com/resources/answers/270665/you_deposit_300_each_month_into_an_account_earning_7_interest_compounded_monthly
What's the point of the link, it does not show the formula
and it is a different question.
Yours:
amount = 300( (1+.07/12)^180 - 1)/(.07/12)
= $95,088.69
To find out how much you will have in the account in 15 years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount in the account
P is the principal amount (the initial deposit)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal amount is $300, the annual interest rate is 7% (or 0.07), the interest is compounded monthly (so n = 12), and the number of years is 15 (so t = 15).
Plugging these values into the formula:
A = 300(1 + 0.07/12)^(12*15)
A ≈ $7676.86
Therefore, you will have approximately $7,676.86 in the account after 15 years.
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 in 15 years:
Total Deposits = Monthly Deposit * Number of Months
In this case, the monthly deposit is $300, and the number of months in 15 years would be 15 * 12 = 180.
Total Deposits = $300 * 180
Total Deposits = $54,000
Therefore, you will put a total of $54,000 into the account over 15 years.
To find out how much total interest you will earn, you can subtract the total deposits from the final amount in the account:
Total Interest = Final Amount - Total Deposits
In this case, the final amount is $7,676.86 and the total deposits are $54,000.
Total Interest = $7,676.86 - $54,000
Total Interest = -$46,323.14
Therefore, the total interest you will earn is approximately -$46,323.14. This negative value indicates that you will actually be paying more in deposits than you will receive in interest.
To find the future value of the account after 15 years, we can use the formula for compound interest:
Future Value = P * (1 + r/n)^(nt)
Where:
P = Initial deposit or principal amount ($300 each month)
r = Annual interest rate (7% or 0.07)
n = Number of times interest is compounded per year (monthly, so 12)
t = Number of years (15)
To find the total money you will put into the account, you can multiply the monthly deposit by the number of months in 15 years:
Total Deposits = Monthly Deposit * Number of Months
To find the total interest earned, you can subtract the total deposits from the future value:
Total Interest = Future Value - Total Deposits
Let's calculate each value step by step:
1. Future Value:
Plug in the values from the problem into the compound interest formula:
Future Value = $300 * (1 + 0.07/12)^(12*15)
= $300 * (1.00583)^(180)
≈ $1,047.14
So, you will have approximately $1,047.14 in the account after 15 years.
2. Total Deposits:
Since you deposit $300 each month, and there are 12 months in a year, multiply the monthly deposit by the number of months:
Total Deposits = $300 * 12 * 15
= $54,000
Therefore, you will put a total of $54,000 into the account over 15 years.
3. Total Interest:
Subtract the total deposits from the future value to find the total interest earned:
Total Interest = Future Value - Total Deposits
= $1,047.14 - $54,000
= -$52,952.86
Here, the negative value indicates that the total interest earned is less than the total deposits made.
In conclusion:
- After 15 years, you will have approximately $1,047.14 in the account.
- You will put a total of $54,000 into the account.
- The amount of interest you will earn is -$52,952.86 (negative because it is less than the deposits made).