Final answer:
To calculate the future value of P₈₀₀₀ deposited at the end of each month into a savings account after 2 years at 6% interest compounded monthly, we can use the formula for compound interest. By substituting the given values into the formula and solving for the future value, we find that the amount will be approximately $8,784.58.
Step-by-step explanation:
To calculate the future value of P₈₀₀₀ deposited at the end of each month into a savings account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A = the future value
- P = the principal amount deposited at the end of each month
- r = the annual interest rate (decimal)
- n = the number of times interest is compounded per year
- t = the number of years
In this case, P = P₈₀₀₀, r = 0.06 (6%), n = 12 (compounded monthly), and t = 2 years.
Substituting these values into the formula and solving for A, we get:
A = P₈₀₀₀(1 + 0.06/12)^(12*2)
A = P₈₀₀₀(1 + 0.005)^(24)
A = P₈₀₀₀(1.005)^(24)
Now, we can calculate the value of A by multiplying P₈₀₀₀ by (1.005) raised to the power of 24:
A = P₈₀₀₀ * 1.005^24
Using a calculator, the value of A is approximately $8,784.58. Therefore, P₈₀₀₀ deposited at the end of each month into a savings account will be worth approximately $8,784.58 after 2 years at 6% interest compounded monthly.