Question
Lamar deposited $4000 into an account with 3.2% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 7 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
GPT 3.5
To calculate the amount Lamar will have in the account after 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal 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 for
Given:
P = $4000
r = 3.2% = 0.032
n = 2 (compounded semiannually)
t = 7 years
Plugging the values into the formula:
A = $4000(1 + 0.032/2)^(2*7)
A ≈ $4000(1 + 0.016)^(14)
A ≈ $4000(1.016)^14
A ≈ $4000(1.250792)
A ≈ $5003.17
Therefore, Lamar will have $5003.17 in the account after 7 years.
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal 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 for
Given:
P = $4000
r = 3.2% = 0.032
n = 2 (compounded semiannually)
t = 7 years
Plugging the values into the formula:
A = $4000(1 + 0.032/2)^(2*7)
A ≈ $4000(1 + 0.016)^(14)
A ≈ $4000(1.016)^14
A ≈ $4000(1.250792)
A ≈ $5003.17
Therefore, Lamar will have $5003.17 in the account after 7 years.