Final answer:
To calculate the balance of a single deposit compounded quarterly at a 5% annual interest rate after 6 years, you can use the formula A = P(1 + r/n)^nt. Plugging in the given values, the balance is approximately $1343.92.
Step-by-step explanation:
To calculate the balance of a single deposit compounded quarterly, we can use the formula:
A = P(1 + r/n)nt
A is the balance after time t
P is the principal amount (initial deposit)
r is the annual interest rate (decimal)
n is the number of compounding periods per year
t is the number of years
In this case, the values are:
P = $1000
r = 0.05 (5% as a decimal)
n = 4 (quarterly compounding)
t = 6 years
Plugging these values into the formula, we get:
A = $1000(1 + 0.05/4)4*6
Simplifying the exponents, we have:
A = $1000(1.0125)24
Using a calculator or spreadsheet, we find that A is approximately $1343.92.