Question

To yield $8000 in three years in an investment that pays interest at a rate of 5% per year, compounded semi-annually, how much would you have to invest?​

Answer 1

Answer: To calculate the initial investment required to yield $8000 in three years with a 5% interest rate compounded semi-annually, we can use the compound interest formula:

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

Where:

A = the final amount ($8000)

P = the initial investment (what we want to find)

r = the annual interest rate (5% = 0.05 in decimal form)

n = the number of times interest is compounded per year (semi-annually means 2 times per year)

t = the number of years (3 years)

Now, plug in the values and solve for P:

$8000 = P(1 + 0.05/2)^(2*3)

Now, simplify the equation:

$8000 = P(1.025)^6

Next, isolate P:

P = $8000 / (1.025)^6

Now, calculate (1.025)^6:

(1.025)^6 ≈ 1.161547

Finally, find the initial investment P:

P ≈ $8000 / 1.161547 ≈ $6890.44

So, you would need to invest approximately $6890.44 to yield $8000 in three years with a 5% interest rate compounded semi-annually.