Final answer:
To find the future value of an investment with $5,000 annual payments and an 8% interest rate over 3 years, we apply the future value of an annuity formula.
Step-by-step explanation:
To determine the future value of an investment where $5,000 is invested at the end of each year with an 8% interest rate, we use the future value of an annuity formula. Unfortunately, the question text seems to mix concepts of loans and investments, and also simple interest calculations, which are not applicable to this annuity problem.This calculation will provide the total value of the investments after three years, which compounds annually, unlike simple interest which only applies to static amounts over time.
For an annuity where the deposits are made at the end of the period (ordinary annuity), we use the formula:
FV = P × {((1 + r)^n - 1) / r}
Where:
- FV is the future value of the annuity.
- P is the periodic payment (in this case, $5,000).
- r is the interest rate per period.
- n is the number of periods.
According to the formula, after three years ($n=3$), with an interest of 8% annually ($r=0.08$):
FV = $5,000 × {((1 + 0.08)^3 - 1) / 0.08}
This calculation reveals the total amount Pedro Gonzalez's investment will be worth after three years, embracing the concept of compound interest.
Note that simple interest is not being used here as the question involves a series of investments (annuities), and simple interest would only be used for calculating the interest on a single lump sum amount over time without additional investments.