Question
business invests $10,000 in an account that earns 3.2% interest that is compounded quarterly.
What is the value of the account after 5 years? Round to the nearest cent
What is the value of the account after 5 years? Round to the nearest cent
Answers
GPT 3.5
After 5 years, the value of the account can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $10,000
r = 3.2% or 0.032
n = 4 (quarterly compounding)
t = 5 years
A = $10,000(1 + 0.032/4)^(4*5)
A = $10,000(1 + 0.008)^20
A = $10,000(1.008)^20
A = $10,000 * 1.17167447643
A ≈ $11,716.74
Therefore, the value of the account after 5 years would be approximately $11,716.74.
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $10,000
r = 3.2% or 0.032
n = 4 (quarterly compounding)
t = 5 years
A = $10,000(1 + 0.032/4)^(4*5)
A = $10,000(1 + 0.008)^20
A = $10,000(1.008)^20
A = $10,000 * 1.17167447643
A ≈ $11,716.74
Therefore, the value of the account after 5 years would be approximately $11,716.74.