Answer:
$4550.58.
Step-by-step explanation:
After 7 years, the amount in the bank can be calculated using the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A is the final amount
P is the initial principal amount (which is $3000 in this case)
r is the interest rate (which is 7 percent or 0.07)
n is the number of times interest is compounded per year
1. Compounded Annually:
If interest is compounded annually, n is 1. Plugging in the values into the formula, we get:
A = 3000(1 + 0.07/1)^(1*7)
A = 3000(1.07)^7
A ≈ $4495.65
After 7 years, the amount in the bank would be approximately $4495.65.
2. Compounded Quarterly:
If interest is compounded quarterly, n is 4. Plugging in the values into the formula, we get:
A = 3000(1 + 0.07/4)^(4*7)
A = 3000(1.0175)^28
A ≈ $4522.28
After 7 years, the amount in the bank would be approximately $4522.28.
3. Compounded Monthly:
If interest is compounded monthly, n is 12. Plugging in the values into the formula, we get:
A = 3000(1 + 0.07/12)^(12*7)
A = 3000(1.00583)^84
A ≈ $4535.98
After 7 years, the amount in the bank would be approximately $4535.98.
4. Compounded Continuously:
If interest is compounded continuously, we use the formula:
A = Pe^(rt)
Plugging in the values into the formula, we get:
A = 3000e^(0.07*7)
A ≈ $4550.58
After 7 years, the amount in the bank would be approximately $4550.58.
Please note that these calculations assume that no additional deposits or withdrawals are made during the 7-year period. Also, the values are approximate due to rounding.