Find the ending balance in a account that opens with 6,480, earns 8.5% interest compounded monthly, and is held for 15 years.
To find the ending balance of an account with the given parameters, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Ending balance
P = Principal amount (initial balance)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Let's plug in the values given in the question:
P = $6,480
r = 8.5% = 0.085 (annual interest rate in decimal form)
n = 12 (since interest is compounded monthly)
t = 15 (number of years)
Now we can substitute these values into the formula and calculate the ending balance:
A = 6480(1 + 0.085/12)^(12*15)
First, let's solve the expression within the parentheses:
0.085/12 ≈ 0.00708333
1 + 0.00708333 ≈ 1.00708333
Now, let's calculate the exponent:
12 * 15 = 180
Finally, let's substitute these values into the formula:
A = 6480(1.00708333)^180
Calculating this expression will give us the ending balance of the account.