80.3k views
2 votes
$3000 are invested in a bank account at an interest rate of 7 percent per year.

Find the amount in the bank after 7 years if interest is compounded annually.

Find the amount in the bank after 7 years if interest is compounded quarterly.

Find the amount in the bank after 7 years if interest is compounded monthly.

Finally, find the amount in the bank after 7 years if interest is compounded continuously .

User Tillebeck
by
8.8k points

2 Answers

4 votes

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.

User Ergo
by
8.9k points
2 votes

Final answer:

The amount in the bank after 7 years with interest compounded annually is $4,847.89. With interest compounded quarterly, it is $4,894.18. With interest compounded monthly, it is $4,919.11. With continuous compounding, it is $4,925.51.

Step-by-step explanation:

To find the amount in the bank after 7 years with an interest rate of 7 percent compounded annually, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P = $3000, r = 7%, n = 1, and t = 7. Plugging these values into the formula, we get:

A = 3000(1 + 0.07/1)^(1*7) = $4847.89

To find the amount in the bank after 7 years with interest compounded quarterly, we use the same formula but with n = 4:

A = 3000(1 + 0.07/4)^(4*7) = $4894.18

To find the amount in the bank after 7 years with interest compounded monthly, we use the same formula but with n = 12:

A = 3000(1 + 0.07/12)^(12*7) = $4919.11

Finally, to find the amount in the bank after 7 years with continuous compounding, we use the formula A = Pe^(rt), where e is the mathematical constant approximately equal to 2.71828:

A = 3000e^(0.07*7) = $4925.51

User AlfredBaudisch
by
8.6k points

No related questions found