You can calculate the $3,000 per-year deficit if it had been invested. The formula for compound interest is A = P (1+r). A represents the total amount of money, A the last amount, P the initial principal, or investment amount, and r the annual interest rate in decimal. n is how many years.

Let’s say that we take a 7% annual interest rate (the market rate for return in this case), and the result is: A = $3000 (1+0.07)15 = 85,907.33

It would mean that the $3,000 annual deficit had to be invested each year at a 7% rate. This would have made it $85,907.33 over the course of 15 years.

- The process of compounding, where interest is earned both on the original investment as well as on the accrued interest. Compounded interest means that compound interest will increase investment growth by increasing the length of an investment.

If $3,000 were invested at 7% for 15 years, then the first year would yield $210. (7% on $3,000). The $3,000 principal and $210 interest earned in the first year would bring in $315.90 (7% of $3.210) in interest the second year. It continues with interest earning in each year adding to the principal, as well as interest being earned the following year.

As a result, the final amount received ($85,907.33) is greater than it would be without compounding, which is calculated by (3000*15 = 45000)

- You can calculate the potential return for the $20,000 investment by using the future-value formula. This calculates future value based on fixed interest rates. FV = PV (1+r)n FV stands for future value. PV or the initial investment is PV, r the annual interest rate and n the time period.

The FV in this example is $20,000 (1+0.07)20 = $70,000. This means the investment will double over 20 years.

- The formula for the present worth of an annuity can be used to indicate your expected return, and whether you should accept or reject it. It calculates the amount of future payments, based on an interest rate fixed.

PV = (PMT / r) * (1 – (1 / (1 + r)^n)) Where PV is the present value, PMT is the payment amount, r is the annual interest rate, and n is the number of payments.

In this case, PV = ($8,000 / 0.07) * (1 – (1 / (1 + 0.07)^17)) = $100,000

Therefore, the annuity will not offer any additional value but would only return the amount invested

- It is the concept that money’s time value is different depending on its receipt. Because money can be invested to earn interest, it is more valuable than money that has been received now. This is a key concept in financial planning. It can be used to help people make investment and spending decisions based on their timeline and goals.