Final answer:
The present value and compound interest involve calculations based on the rate and frequency of compounding. The present value for an investment with a future value of $16,000, compounded monthly at a 4.5% annual rate over 8 years, can be found using the present value formula. Compound interest is the difference between the future value and the present value.
Step-by-step explanation:
The question concerns the calculation of the present value for an investment, given a future value amount that has been compounded. Compound interest is fundamentally an interest rate calculation on the principal plus the accumulated interest over time. To find the present value, we can apply the formula for present value which includes the future value, the nominal interest rate, and the number of compounding periods.
Given:
The formula for present value (PV) is:
PV = Future Value / (1 + r/n)nt
Where:
Substituting the given values:
PV = 16000 / (1 + 0.045/12)12*8
Calculating this gives the present value, which represents the current worth of the future investment. The compound interest can then be found by subtracting this present value from the future value.