Final answer:
The question deals with the time value of money within the Mathematics field at the College level. It demonstrates that due to compound interest, $1,000 invested today is worth more one year from now than $1,000 received in the future with a 12% interest rate.
Step-by-step explanation:
The subject of the question is Mathematics, and it pertains to the concept of time value of money, which is relevant for students at the College level.
When John invests $1,000 today and expects to receive $1,000 in the future, we must consider the present value of future money. If the prevailing interest rate is 12%, he would only need to invest $964 now to receive $1,080 a year from now, which is the future value of that investment. Therefore, the $1,000 he invests today will effectively be worth more than the $1,000 he receives in the future due to the growth of investment. Indeed, at a 12% return rate, his $1,000 investment now will grow to $1,120 in a year, showing the power of compound interest.
Understanding the concept of the time value of money and compound interest is critical. It highlights that a dollar today is worth more than a dollar in the future because money can earn interest and therefore grow over time. This is precisely why starting to save and invest early, like in the case of investing $3,000 at a 7% annual rate, can lead to substantial growth in wealth over the long term. Compound interest can significantly increase your investment's value, turning a single $3,000 investment into $44,923 over 40 years.