An initial investment of $12,000 is appreciated for 5 years in an account that earns 7% interest, compounded quarterly. Find the amount of money in the account at the end of the period
12,000*(1.0175)^20 = $16,977.34
To find the amount of money in the account at the end of the period, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is invested for
In this case, the initial investment (P) is $12,000, the interest rate (r) is 7% (or 0.07 as a decimal), and the money is invested for 5 years (t).
Since the interest is compounded quarterly, the number of times the interest is compounded per year (n) is 4.
Now let's plug in the values into the formula and calculate the future value (A):
A = $12,000 * (1 + 0.07/4)^(4 * 5)
Performing the calculations:
A = $12,000 * (1.0175)^(20)
A ≈ $12,000 * 1.395857096
A ≈ $16,750.29
So, at the end of the 5-year period, the amount of money in the account would be approximately $16,750.29.