suppose your friends parents invest 20,000 in an account paying 7% compounded annually what will the balance be after 6 years
b = 20000 (1 + .07)^6
To calculate the balance after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final balance
P = the initial investment
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the initial investment (P) is $20,000, the annual interest rate (r) is 7% (0.07 as a decimal), the interest is compounded annually (n = 1), and the number of years (t) is 6.
Now, let's substitute the values into the formula:
A = 20,000(1 + 0.07/1)^(1*6)
A = 20,000(1 + 0.07)^6
A = 20,000(1.07)^6
Calculating:
A ≈ 20,000(1.07)^6
A ≈ 20,000(1.503),
A ≈ $30,060
Therefore, the balance after 6 years will be approximately $30,060.
To determine the balance after 6 years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance) after the specified time period
P = the principal amount (initial investment) = $20,000
r = the annual interest rate as a decimal = 7% = 0.07
n = the number of times the interest is compounded per year = 1 (compounded annually)
t = the number of years the money is invested for = 6
Let's plug these values into the formula and calculate:
A = 20,000(1 + 0.07/1)^(1*6)
A = 20,000(1 + 0.07)^6
A = 20,000(1.07)^6
A ≈ 20,000(1.4886)
A ≈ $29,772
So, the balance after 6 years would be approximately $29,772.