determine the amount of an investment if $500 is invested at an interest rate of 4.25% compounded quarterly for 12 years?
Use
P(1+r)^n
Since interest is compounded quarterly,
the interest rate has to be divided by 4 to get the quarterly rate. The number of periods (years) has to be multiplied by 4 to get quarters.
P=500
R=(1+0.0425/4)
n=12*4=48
So
500*(1+0.0425/4)^48
=830.41
Why did the investor bring a ladder to the bank? Because they wanted to make sure their interest rates were through the roof! Now, let me do the math for you.
To determine the amount of an investment, we'll use the compound interest formula: A = P(1 + r/n)^(nt), where:
A is the final amount,
P is the principal amount (initial investment),
r is the annual interest rate (as a decimal),
n is the number of times interest is compounded per year, and
t is the number of years.
In this case, the principal amount (P) is $500, the annual interest rate (r) is 4.25% (0.0425 as a decimal), the interest is compounded quarterly (n = 4), and the investment is for 12 years (t = 12).
Now let's calculate it:
A = 500(1 + 0.0425/4)^(4*12)
A = 500(1.010625)^(48)
A ≈ 500(1.647010)
A ≈ $823.51
So, the amount of the investment after 12 years would be approximately $823.51. That's surely nothing to clown around with!
To determine the amount of an investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $500
r = 4.25% = 0.0425 (as a decimal)
n = 4 (quarterly compounding)
t = 12
Now we can plug in the values and calculate the future value (A):
A = 500(1 + 0.0425/4)^(4*12)
A = 500(1 + 0.010625)^(48)
A = 500(1.010625)^(48)
A ≈ $716.23
Therefore, the amount of the investment after 12 years would be approximately $716.23.
To determine the amount of an investment, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $500, the annual interest rate (r) is 4.25% (or 0.0425 as a decimal), the interest is compounded quarterly (n = 4), and the investment period (t) is 12 years.
Plugging these values into the formula:
A = 500(1 + 0.0425/4)^(4*12)
Calculating the exponent first:
A = 500(1 + 0.010625)^(48)
Evaluating the parentheses:
A = 500(1.010625)^(48)
Using a calculator or spreadsheet, calculate the value inside the parentheses to the power of 48, and then multiply by 500:
A ≈ 500(1.677101)
A ≈ 838.55
Therefore, the amount of the investment after 12 years would be approximately $838.55.