The expression that gives the balance in the account after 3 years is:
C. 400(1+0.05)(1 + 0.05)(1+0.05)
Which expression gives the balance in the account after 3 years?
The expression 400(1+0.05)(1+0.05)(1+0.05) represents the compound interest calculation for Benjamin's savings account over three years.
Let's break down the expression step by step:
400 represents the initial investment amount. Benjamin initially invests $400 in the savings account.
(1+0.05) represents the factor for calculating the interest earned each year. The interest rate is given as 5%, so adding 0.05 to 1 represents a 5% increase.
Multiplying (1+0.05) three times represents the compound interest calculation for three years. Each time the expression is multiplied, it accounts for the interest earned in the subsequent year.
By multiplying the initial investment of $400 by the compound interest factor (1+0.05) three times, the expression calculates the total balance in the account after three years. This accounts for the annual interest earned on the initial investment.
To calculate the result, substitute the values into the expression:
400(1+0.05)(1+0.05)(1+0.05) = 400(1.05)(1.05)(1.05) = 400(1.157625) ≈ 463.05
Therefore, the balance in Benjamin's savings account after three years would be approximately $463.05, assuming the interest is compounded annually at a rate of 5%.
Benjamin invests $400 in a savings account that earns 5% interest each year.
Which expression gives the balance in the account after 3 years?
Choose 1 answer:
A 400+ 0.05 -0.05 -0.05
B 400 - 0.05 - 0.05 -0.05
C 400+ (1 + 0.05)(1+0.05)(1 + 0.05)
D 400(1+0.05)(1 + 0.05)(1+0.05)