Find the compound interest on 650 in 5 years at 4% per annum
What is
650(1.04)^5 - 650 ?
Caculate
Why did the math book look sad? Because it had too many problems! But don't worry, I can help you with this one. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the number of years.
So, in your case:
P = $650
r = 4% = 0.04 (as decimal)
n = 1 (compounded annually)
t = 5 years
Let's calculate the compound interest and put a smile on that math book's face!
A = 650(1 + 0.04/1)^(1*5)
A = 650(1 + 0.04)^5
A = 650(1.04)^5
A ≈ 650(1.21665)
A ≈ $791.32
The compound interest on $650 at 4% per annum for 5 years is approximately $791.32.
Remember, math doesn't always have to be sad. It can be fun, too!
To calculate the compound interest, we can use the formula:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $650
r = 4% per annum = 0.04 (as a decimal)
n = 1 (compounded annually)
t = 5 years
Let's calculate the compound interest step-by-step:
Step 1: Calculate the future value (A) using the compound interest formula.
A = 650(1 + 0.04/1)^(1*5)
A = 650(1 + 0.04)^5
A = 650(1.04)^5
A = 650(1.2166529024)
A ≈ 790.85
Step 2: Calculate the compound interest by subtracting the principal investment amount (P) from the future value (A).
Compound Interest = A - P
Compound Interest ≈ 790.85 - 650
Compound Interest ≈ $140.85
Therefore, the compound interest on $650 in 5 years at 4% per annum is approximately $140.85.
To find the compound interest on a principal amount over a certain period of time, you need to use the compound interest formula:
A = P * (1 + r/n)^(n*t)
Where:
A = the final amount (including the principal and interest)
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is 650, the annual interest rate (r) is 4% (or 0.04 as a decimal), and the time period (t) is 5 years. Since the question doesn't specify the compounding frequency, we'll assume it is compounded annually (n = 1).
Now, let's calculate the compound interest step by step:
Step 1: Convert the annual interest rate to decimal form:
r = 4% = 0.04
Step 2: Plug in the values into the compound interest formula:
A = 650 * (1 + 0.04/1)^(1*5)
Step 3: Simplify and compute the compound interest:
A = 650 * (1 + 0.04)^5
A = 650 * (1.04)^5
A = 650 * 1.21665
A ≈ 791.72
Step 4: Calculate the compound interest by subtracting the principal amount from the final amount:
Compound Interest = A - P
Compound Interest = 791.72 - 650
Compound Interest ≈ 141.72
Therefore, the compound interest on 650 in 5 years at a rate of 4% per annum is approximately 141.72.