Answer:
Explanation:
Hello! To find the number of years it took for the initial deposit of $1500 to grow to $4936 with a 6% interest rate compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal (initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, we have:
A = $4936
P = $1500
r = 6% = 0.06
n = 4 (quarterly compounding)
Substituting the values into the formula, we get:
$4936 = $1500(1 + 0.06/4)^(4t)
To solve for t, we need to isolate it on one side of the equation. Let's divide both sides by $1500:
4936/1500 = (1 + 0.06/4)^(4t)
Now, let's simplify the equation:
3.29067 = (1.015)^(4t)
To solve for t, we can take the logarithm of both sides. Let's use the natural logarithm (ln):
ln(3.29067) = ln((1.015)^(4t))
Using the logarithmic property, we can bring down the exponent:
ln(3.29067) = 4t * ln(1.015)
Now, divide both sides by 4 * ln(1.015) to solve for t:
t = ln(3.29067) / (4 * ln(1.015))
Using a calculator, we find:
t ≈ 8.36 years
Rounding to the nearest year, we can conclude that it took approximately 8 years for the initial deposit to grow to $4936.