Manually calculate the compound interest on an investment of $8500 at 6% interest, compounded semiannually, for 18 mo.

Manually, like with pencil and paper?

Interest= 3*8500*.03 + 8500*.03^2 + 8500(.03^3)=772.88

That is a lot of multiplying manually.

To calculate the compound interest on an investment, we can use the formula:

A = P(1 + r/n)^(nt)

where:
A = the final amount including interest
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = time in years

In this case, we have:
P = $8500
r = 6% or 0.06
n = 2 (semiannual compounding - twice per year)
t = 18 months = 18/12 = 1.5 years

Substituting these values into the formula, we get:

A = 8500(1 + 0.06/2)^(2*1.5)

Calculating further:

A = 8500(1 + 0.03)^3

A = 8500(1.03)^3

A = 8500 * 1.092727

A = $9278.36 (rounded to two decimal places)

Now, to find the compound interest, we subtract the principal amount from the final amount:

Compound Interest = A - P

Compound Interest = 9278.36 - 8500

Compound Interest = $778.36

Therefore, the compound interest on an investment of $8500 at 6% interest, compounded semiannually, for 18 months is $778.36.

To manually calculate the compound interest on an investment, you can use the formula:

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 (in decimal form)
n = the number of times interest is compounded per year
t = the number of years

In this case, the principal amount (P) is $8500, the interest rate (r) is 6% or 0.06, the interest is compounded semiannually, so the compounding periods per year (n) would be 2, and the time (t) is 18 months or 1.5 years.

Let's plug in these values into the formula:

A = $8500(1 + 0.06/2)^(2 * 1.5)

Step 1: Calculate the value inside the parentheses, i.e., (1 + 0.06/2):

(1 + 0.06/2) = 1.03

Step 2: Calculate the exponent, i.e., (2 * 1.5):

(2 * 1.5) = 3

Step 3: Substitute the values back into the formula:

A = $8500(1.03)^3

Step 4: Calculate the value of (1.03)^3:

(1.03)^3 = 1.0927

Step 5: Calculate the future value:

A = $8500 * 1.0927

A ≈ $9287.95

Therefore, the compound interest on an investment of $8500 at 6% interest, compounded semiannually, for 18 months is approximately $9287.95 - $8500 = $787.95.