You have a savings account with 7.5 percent annual interest rate and invest $50 a month into the account. How much will the account have in it (assuming no withdrawals) after two years?
To calculate how much will be in the account after two years, we first need to calculate the total amount of money deposited into the account over the two years.
In two years, you will deposit $50 every month for a total of 24 months. So the total amount deposited will be:
$50 x 24 = $1200
Now, we need to calculate the interest earned on the initial deposit and subsequent monthly deposits over the two years. To simplify things, let's assume the interest is compounded monthly.
The formula to calculate the future value of a savings account with monthly deposits is:
FV = P(1 + r/n)^(nt)
Where:
FV = future value of the account
P = principal amount (initial deposit)
r = annual interest rate (7.5% or 0.075)
n = number of times interest is compounded per year (12 for monthly)
t = number of years
Let's plug in the values:
P = $0 (initial deposit)
r = 0.075
n = 12
t = 2
FV = $0 x (1 + 0.075/12)^(12*2)
FV = $0 x (1 + 0.00625)^24
FV = $0 x (1.00625)^24
FV = $0 x 1.161505
FV ≈ $0
So after two years, the account will have approximately $0 in it, assuming no withdrawals were made. This is because no initial deposit was made, and the interest earned on the monthly deposits alone was not enough to accumulate a significant amount.