if $6000 is invested at 3% compounded quarterly, what is the amount after 6yrs?
To calculate the amount after 6 years when $6000 is invested at 3% compounded quarterly, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future amount (final balance)
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $6000
r = 3% or 0.03 (as a decimal)
n = 4 (quarterly compounding)
t = 6 years
Plugging these values into the formula:
A = 6000(1 + 0.03/4)^(4*6)
A = 6000(1 + 0.0075)^(24)
A = 6000(1.0075)^(24)
Calculating this expression, we get:
A ≈ $7,065.86
Therefore, the amount after 6 years will be approximately $7,065.86.
To calculate the amount after 6 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including principal and interest)
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 = $6000
r = 3% = 0.03 (since it's given as a percentage, we divide by 100)
n = 4 (compounded quarterly, so 4 times a year)
t = 6 years
Plugging these values into the formula, we get:
A = 6000(1 + 0.03/4)^(4*6)
Now, let's solve this equation step by step:
Step 1: Divide the annual interest rate by the number of compounding periods per year:
0.03/4 = 0.0075
Step 2: Multiply the number of compounding periods per year by the number of years:
4*6 = 24
Step 3: Calculate the parenthesis:
(1 + 0.0075)^(24) = (1.0075)^(24)
Step 4: Raise the base to the power of 24 using a calculator. This results in approximately 1.18874846.
Step 5: Multiply the principal by the result from step 4:
A = $6000 * 1.18874846
Step 6: Calculate the final amount:
A ≈ $7,127.49
Therefore, the amount after 6 years will be approximately $7,127.49 when $6000 is invested at 3% compounded quarterly.