Final answer:
The question is about calculating the future value of a $1,000,000 investment in GLD (a gold-backed ETF) from 2005 to 2018. Without historical performance data, we cannot compute the exact figure. However, the principles of compound interest and the impact of changes in interest rates on bond prices are explained.
Step-by-step explanation:
Understanding Investment Growth and Compound Interest
Investing $1,000,000 in GLD (a gold-backed ETF) at the beginning of 2005 and calculating its worth at the end of 2018 requires some historical data about GLD's performance, which is not provided in your question. Therefore, the calculation cannot be made accurately without that specific information. However, I can demonstrate how to estimate the future value of an investment using compound interest, assuming a certain average annual growth rate. Let's use the power of compound interest as an example:
Suppose you have an annual growth rate of 3.5% and invest $1,000. The future value of this investment after a certain number of years can be calculated using the following formula:
Future Value = Present Value * (1 + growth rate)^number of years
For the example of $1,000 invested at the time Columbus sailed to America, which is more than 500 years ago, you would use a high number of years in the calculation. The growth of this investment would be immense over such a long timeline, possibly comparing to the wealth of today's richest individuals or the GDP of entire countries.
Now, regarding bond investments and changes in interest rates, if overall market rates increase, the price of an existing bond with a lower fixed interest rate tends to decrease because newer bonds are available that pay more interest. If you can get a 12% return through an alternative investment, you would not pay more than that investment's present value ($964) for a $1,000 bond that yields less. The principle is that as interest rates go up, the price of existing bonds goes down - and vice versa.
Lastly, demonstrating the impact of inflation on purchasing power: $1 in 1955 required $8.57 to have the same purchasing power in 2012. This reflects the decrease in the value of money over time due to inflation. On the other hand, starting to save money early and benefiting from compound interest can lead to significant gains, as an initial investment of $3,000 at a 7% annual return could grow to nearly $44,923 over 40 years.
In the context of compound interest, if you want to have $10,000 in your bank account after ten years, and the bank offers a 10% compounded annually interest rate, you can calculate the required initial investment using the formula for the present value of a future sum:
Present Value = Future Value / (1 + interest rate)^number of years
This financial tool is a powerful concept to understand for efficient financial planning.