Complete the following using compound future value. (Round your answers to the nearest cent.)
Time- 14 years
Principal- $17,500
Rate- 2%
Compounded- annually
Amount- ?
Interest- ?
17,500(1 + 0.2)^14 = 224,685.23
To calculate the compound future value, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Amount after compound interest
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $17,500
r = 0.02 (2% expressed as a decimal)
n = 1 (compounded annually)
t = 14 years
Using these values, we can substitute into the formula:
A = 17,500(1 + 0.02/1)^(1*14)
A = 17,500(1 + 0.02)^14
Calculating:
A ≈ 17,500(1.02)^14
A ≈ 17,500(1.294618)
A ≈ 22,676.07
The compound future value after 14 years is approximately $22,676.07.
To calculate the interest, we can subtract the principal amount from the compound future value:
Interest = A - P
Interest ≈ 22,676.07 - 17,500
Interest ≈ 5,176.07
The interest earned after 14 years is approximately $5,176.07.
To calculate the compound future value, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = Future value
P = Principal amount
r = Annual interest rate
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $17,500
r = 2% (or 0.02 in decimal form)
n = 1 (compounded annually)
t = 14 years
Plugging in these values into the formula, we can calculate the future value (amount) and the interest earned.
First, let's calculate the future value (amount):
A = 17,500(1 + 0.02/1)^(1*14)
A = 17,500(1 + 0.02)^14
A = 17,500(1.02)^14
A ≈ 17,500(1.305948)
A ≈ $22,824.22
Therefore, the compound future value (amount) after 14 years is approximately $22,824.22.
Next, let's calculate the interest earned:
Interest = Future value - Principal
Interest = $22,824.22 - $17,500
Interest ≈ $5,324.22
Therefore, the interest earned after 14 years is approximately $5,324.22.