Find the ending balance in an account that opens with $5,000, earns 7.5% interest compounded quarterly, and is held for 20 years. (Round your answer to the nearest cent.)
To find the ending balance in the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the ending balance
P = the principal amount (initial balance)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $5,000
r = 7.5% = 0.075
n = 4 (compounded quarterly)
t = 20 years
Plugging in these values into the formula, we have:
A = $5,000(1 + 0.075/4)^(4*20)
Now, we can simplify and calculate the value.
A = $5,000(1.01875)^(80)
Using a calculator, we can raise 1.01875 to the power of 80 and then multiply it by $5,000 to get the ending balance. Rounding the final answer to the nearest cent gives us the desired result.