Phillip opened a savings account with an annual interest rate of 8% and an initial deposit of $3500. If his interest is compounded quarterly, how much is in Jeffrey’s account after 2 years? Round your answer to the nearest cent.
interest compounded quarterly: A equals P left parenthesis 1 plus r over 4 right parenthesis to the power of 4 t end exponent
A=P(1+r/4)^4t
just plug the values into your formula , then let your calculator take over
A = 3500(1 + .08/4)^8
= 3500(1.02)^8
= ...
1.56
To calculate the amount in Jeffrey's account after 2 years with quarterly compounding interest, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Amount in the account after interest
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, P = $3500, r = 8% or 0.08, n = 4 (quarterly compounding), and t = 2 years.
Substituting the given values into the formula, we have:
A = 3500(1 + 0.08/4)^(4*2)
Now let's calculate it step by step:
First, divide the annual interest rate (8%) by the number of compounding periods per year (4) to get the quarterly interest rate:
Quarterly interest rate = 0.08 / 4 = 0.02
Next, add 1 to the quarterly interest rate:
1 + 0.02 = 1.02
Now, raise this result to the power of the total number of compounding periods (4) multiplied by the number of years (2):
(1.02)^(4*2) = (1.02)^8 ≈ 1.171614
Finally, multiply the principal amount (P) by this result to get the final amount in the account:
A = 3500 * 1.171614 ≈ $4096.15
Therefore, Jeffrey's account would have approximately $4096.15 after 2 years, rounded to the nearest cent.