Answer:
Sure, I'd be happy to help!
The equation for the total amount after 4 years, assuming an interest rate of 6.2% and compounding:
$$
A = P \times (1 + r/n)^(n\times t)
$$
Where:
A = Total amount after 4 years
P = Principal amount of $3,000
r = Interest rate of 6.2%
n = Number of times interest is compounded per year
t = Time in years (4 years in this case)
Now, we need to determine the value of n, which depends on the compounding frequency.
a. Annually:
n = 1 (since interest is compounded once a year)
b. Quarterly:
n = 4 (since interest is compounded once a quarter)
c. Monthly:
n = 12 (since interest is compounded once a month)
d. Continuously:
n = ∞ (since interest is compounded continuously)
So, the equation for the total amount after 4 years, assuming an interest rate of 6.2% and compounding:
$$
A = 3,000 \times (1 + 0.062/1)^(1\times 4) = 3,000 \times 1.248 = 3,744
$$
Total amount after 4 years: $3,744
Explanation: