Answer:
To calculate the interest rate of the savings account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (in this case, $4300)
P = the principal amount (initial investment, in this case, $3800)
r = annual interest rate (what we need to find)
n = number of times interest is compounded per year (quarterly, so 4 times)
t = number of years (in this case, 2 years)
Plugging in the given values into the formula, we have:
$4300 = $3800(1 + r/4)^(4*2)
Simplifying further:
$4300/$3800 = (1 + r/4)^8
Dividing both sides by $3800:
1.1316 ≈ (1 + r/4)^8
Taking the eighth root of both sides:
(1.1316)^(1/8) ≈ 1 + r/4
Subtracting 1 from both sides:
(1.1316)^(1/8) - 1 ≈ r/4
Multiplying both sides by 4:
4[(1.1316)^(1/8) - 1] ≈ r
Calculating the expression on the left side:
4[(1.1316)^(1/8) - 1] ≈ 0.0310
Therefore, the interest rate of the savings account is approximately 3.10%.
Explanation: