2. The interest on $6,000 at 6 percent compounded semiannually for 8 years is: (Use table in the handbook) (Points : 1)
To calculate the interest on $6,000 at 6% compounded semiannually for 8 years, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested/borrowed for
In this case, we have:
P = $6,000
r = 6% = 0.06 (as a decimal)
n = 2 (semiannually)
t = 8 years
Substituting these values into the formula:
A = $6,000 * (1 + 0.06/2)^(2*8)
Now, let's calculate:
A = $6,000 * (1 + 0.03)^(16)
A = $6,000 * (1.03)^(16)
To find the value of (1.03)^(16), we can consult a table in the handbook or use a calculator. The value comes out to be approximately 1.603683907.
Substituting this value back into the formula:
A = $6,000 * 1.603683907
A = $9,622.10
Therefore, the future value of the investment, including interest, is $9,622.10. To find the interest, we subtract the principal amount:
Interest = $9,622.10 - $6,000
Interest = $3,622.10
Therefore, the interest on $6,000 at 6%, compounded semiannually for 8 years, is $3,622.10.
To find the interest on $6,000 at 6 percent compounded semiannually for 8 years using a table, you will need to use the compound interest formula:
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 = $6,000, r = 0.06 (6 percent as a decimal), n = 2 (compounded semiannually), and t = 8 years.
Plug in these values into the formula:
A = 6000(1 + 0.06/2)^(2*8)
Now, use the table in the handbook to find the value of (1 + 0.06/2)^(2*8) and calculate the final amount A.
The table should provide the values for raising a base to different powers. In this case, you need to find the power of (1 + 0.06/2)^(2*8), which is 128. Use the table to find the value corresponding to the power of 128.
Once you have obtained this value, multiply it by the principal amount ($6,000) to get the final amount (A). The difference between the final amount and the principal will give you the interest earned on the investment.