Final answer:
To reach $75,000 in 6 years with an 11% annual interest rate compounded quarterly, the present value calculation shows that the company needs to invest approximately $24,180.28 today.
Step-by-step explanation:
The student's question pertains to the calculation of the present value required to achieve a future amount of money based on the compound interest formula. To find out how much needs to be invested today to reach $75,000 in 6 years with an annual interest rate of 11% compounded quarterly, we must use the formula for the present value of a future sum:
Present Value (PV) = Future Value (FV) / (1 + r/n)nt
Where:
- FV is the future value, which is $75,000
- r is the annual interest rate, which is 0.11
- n is the number of times the interest is compounded per year, which is 4 (quarterly)
- t is the number of years the money is invested, which is 6
Now, substituting the given values:
PV = $75,000 / (1 + 0.11/4)4*6
Let's calculate the denominator first:
(1 + 0.11/4)4*6 = (1 + 0.0275)24 = 1.027524
Now we can calculate:
PV = $75,000 / 1.027524
PV ≈ $75,000 / 3.1021 ≈ $24,180.28
The company should invest approximately $24,180.28 today to have $75,000 in 6 years with a compound interest rate of 11% compounded quarterly.