Find the value after five years of a $3,000 savings account that pays 3% interest compounded yearly. Round the answer to two decimal places.(1 point)
The formula to calculate the future value of an investment with compound interest is given by:
A = P(1 + r/n)^(n*t)
Where:
A = future value
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, P = $3,000, r = 0.03 (3% expressed as a decimal), n = 1 (compounded yearly), and t = 5 years.
Plugging in the values, we have:
A = 3000(1 + 0.03/1)^(1*5)
A ≈ 3000(1 + 0.03)^(5)
A ≈ 3000(1.03)^(5)
A ≈ 3000(1.1592740743)
A ≈ 3477.82
Therefore, the value after five years of a $3,000 savings account that pays 3% interest compounded yearly is approximately $3,477.82.
explain
Sure!
Compound interest is when interest is calculated on both the initial amount of money (called the principal amount) and any accumulated interest. In this case, we have a savings account with a principal amount of $3,000 and an annual interest rate of 3%. The interest is compounded yearly, meaning it is calculated once a year.
To find the future value of this investment after five years, we can use the formula A = P(1 + r/n)^(n*t), where A represents the future value, P represents the principal amount, r represents the annual interest rate, n represents the number of times the interest is compounded per year, and t represents the number of years.
By plugging in the given values, we have A = 3000(1 + 0.03/1)^(1*5). We simplify this to A ≈ 3000(1 + 0.03)^(5). To further calculate, we use the value 1.03 (1 + 0.03) raised to the power of 5, resulting in 1.03^5 ≈ 1.1592740743.
Finally, we multiply the principal amount, $3,000, by the calculated value to find the future value. A ≈ 3000(1.1592740743) ≈ 3477.82.
Hence, after five years, the savings account will have a value of approximately $3,477.82.
i dont understand
I apologize for any confusion. Let me explain the process in simpler terms.
We have a savings account with $3,000 initial deposit. The account pays 3% interest per year, which means that each year, the amount of money in the account increases by 3% of its current value.
After one year, the account would have the initial deposit of $3,000 plus 3% of $3,000, which is $90. This means the total amount in the account after one year would be $3,000 + $90 = $3,090.
To find the amount after five years, we need to repeat this calculation five times.
After the second year, the amount would be the previous amount of $3,090 plus 3% of $3,090. This gives us $3,090 + 3% of $3,090, which is $93.30. So, after the second year, the total amount in the account would be $3,090 + $93.30 = $3,183.30.
Similarly, after the third year, the amount would be the previous amount of $3,183.30 plus 3% of $3,183.30. After the fourth year, we would add 3% of the previous amount, and after the fifth year, we would add 3% of the previous amount again.
To simplify this calculation, we can use the formula for compound interest, which is A = P(1 + r/n)^(n*t), as mentioned before. By plugging in the values, we find that after five years, the total amount in the account would be approximately $3,477.82.
I hope this explanation is clearer.
how do you do the equation
To calculate the future value using the compound interest formula A = P(1 + r/n)^(n*t), follow these steps:
1. Identify the values:
- P = principal amount (initial deposit) = $3,000
- r = annual interest rate (as a decimal) = 0.03
- n = number of times the interest is compounded per year (compounded yearly in this case) = 1
- t = number of years = 5
2. Plug in the values into the formula:
A = 3000(1 + 0.03/1)^(1*5)
3. Simplify the expression within the parentheses:
A = 3000(1 + 0.03)^(5)
4. Calculate the value of (1 + 0.03) raised to the power of 5, which is (1.03)^5 = 1.1592740743 (rounding it to 10 decimal places).
5. Now substitute this value back into the formula:
A ≈ 3000 * 1.1592740743
6. Multiply the principal amount ($3,000) by the value obtained to find the future value:
A ≈ 3000 * 1.1592740743 ≈ 3477.82222222
7. Round the answer to two decimal places, as requested:
A ≈ $3,477.82
Therefore, after five years, the value of the savings account will be approximately $3,477.82.