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?
To calculate the amount in the account in 35 years, the total money you put into the account, and the total interest you earn, we can use the formula for calculating compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
a) To calculate how much you will have in the account in 35 years, we can use the formula above. The initial deposit is $300, the annual interest rate is 8% (or 0.08 in decimal form), and interest is compounded monthly, so n = 12. Plugging these values in, we get:
A = 300(1 + 0.08/12)^(12*35)
A = 300(1 + 0.0066667)^(420)
A = 300(1.0066667)^(420)
A ≈ $1,528,729.49
Therefore, you will have approximately $1,528,729.49 in the account in 35 years.
b) To calculate the total money you will put into the account, we can multiply the monthly deposit by the number of months in 35 years:
Total Money = Monthly Deposit * Number of Months
Total Money = $300 * (12 * 35)
Total Money = $378,000
Therefore, you will put a total of $378,000 into the account.
c) To calculate the total interest earned, we can subtract the total money you put into the account from the future value of the investment:
Total Interest = Future Value - Total Money
Total Interest = $1,528,729.49 - $378,000
Total Interest = $1,150,729.49
Therefore, you will earn a total of $1,150,729.49 in interest.