You deposit $1000 each year into an account earning 8% compounded annually.
a. How much will you have in the account in 10 years?
b. How much total money will you put into the account?
c. How much total interest will you earn?
How
To answer these questions, we will need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested
Let's calculate each of the values requested:
a. How much will you have in the account in 10 years?
In this case, the principal investment amount (P) is $1000, the annual interest rate (r) is 8% (or 0.08 as a decimal), the number of times interest is compounded per year (n) is 1 (compounded annually), and the number of years (t) is 10.
Plugging these values into the compound interest formula:
A = 1000(1 + 0.08/1)^(1*10)
A = 1000(1 + 0.08)^10
A = 1000(1.08)^10
A ≈ $2158.92
Therefore, after 10 years, you would have approximately $2158.92 in the account.
b. How much total money will you put into the account?
In this case, you deposit $1000 each year for 10 years. Therefore, the total money put into the account can be calculated as:
Total Money Deposited = Deposit Year 1 + Deposit Year 2 + ... + Deposit Year 10
Total Money Deposited = $1000 + $1000 + ... + $1000 (10 times)
Total Money Deposited = $1000 * 10
Total Money Deposited = $10,000
Therefore, the total money you would have put into the account is $10,000 over 10 years.
c. How much total interest will you earn?
To calculate the total interest earned, we need to subtract the total money deposited from the future value of the investment (A) calculated in part (a).
Total Interest = A - Total Money Deposited
Total Interest = $2158.92 - $10,000
Total Interest ≈ -$7841.08
The total interest earned would be approximately -$7841.08. Note that the negative sign indicates a loss, as the total money deposited is greater than the future value of the investment.
To calculate the results, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/amount in the account
P = the principal amount (the initial amount deposited)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $1000
r = 8% or 0.08
n = 1 (compounded annually)
t = 10 years
a. How much will you have in the account in 10 years?
Using the formula, we can calculate:
A = $1000(1 + 0.08/1)^(1*10)
A = $1000(1.08)^10
A ≈ $2143.92
So, you will have approximately $2,143.92 in the account after 10 years.
b. How much total money will you put into the account?
Since you are depositing $1000 each year for 10 years, the total amount of money put into the account can be determined by multiplying the annual deposit by the number of years:
Total money = $1000 x 10 = $10,000
So, the total amount you will put into the account is $10,000.
c. How much total interest will you earn?
To calculate the total interest earned, we subtract the total amount of money deposited from the future value of the investment:
Total interest = Future value - Total money deposited
Total interest = $2143.92 - $10,000
Total interest ≈ -$7856.08
Therefore, the total interest you will earn is approximately -$7,856.08. Note that the negative sign indicates that you have paid more in deposits than the interest earned.