1. you deposit $200 into a savings account with interest compounded. annually, the expression 200(1+R)^
2, where R is the interest rate, gives the account balance after 2 years. Expand this expression and simplify. Find the account balance if R=0.04.
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P = 200 (1+R)^n
P = 200 (1.04)^2
= $216.32
To expand and simplify the expression, we use the formula for compound interest:
A = P(1 + R)^t
Where:
A is the account balance,
P is the principal amount (initial deposit),
R is the interest rate (as a decimal),
and t is the number of years.
Given:
P = $200
R = 0.04
t = 2 years
Expanding the expression:
A = 200(1 + 0.04)^2
To simplify a compound interest expression, we need to evaluate the parentheses first:
A = 200(1.04)^2
Now, we can square the expression inside the parentheses:
A = 200(1.0816)
Finally, multiply the principal amount by the simplified expression:
A = $216.32
So, if the interest rate is 0.04, the account balance after 2 years will be $216.32.