Mary just deposited $33,000 in an account paying 7% interest. She plans to leave the money in this account for eight years. How much will she have in the account at the ned of the seventh year?
To find out how much Mary will have in the account at the end of the seventh year, we need to calculate the compound interest earned over the seven-year period.
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money after the given time period
P is the principal amount (initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times the interest is compounded per year
t is the time in years
In this case, Mary deposited $33,000 at an interest rate of 7% (0.07) and plans to leave it in the account for eight years.
Since we want to calculate the amount at the end of the seventh year, we can plug these values into the formula, assuming the interest is compounded annually (n = 1) and t = 7:
A = 33000(1 + 0.07/1)^(1 * 7)
Simplifying the calculation step-by-step:
A = 33000(1.07)^7
A = 33000(1.5089738)
A ≈ $49,776.13
Therefore, at the end of the seventh year, Mary will have approximately $49,776.13 in her account.