Question

Suppose that you are planning for retirement. You want to have exactly $10 million dollars when you retire. You just turned 30 (T=0) and plan to retire on your 65th birthday. For the next 15 years, you can save $18,000 per year (with the first deposit being made one year from now), and at the end of that time (T=15) you plan to buy a car for your child as a gift that will cost $29,000.

Answer 1

The question pertains to planning for retirement and understanding the effects of compound interest and savings strategies to achieve a goal of $10 million by retirement age.

Step-by-step explanation:

When planning for retirement and aiming to have $10 million dollars at retirement, starting at age 30 and retiring at 65, it is crucial to understand compound interest and saving strategies. By investing $18,000 annually for 15 years and buying a car for $29,000 at T=15, the scenario involves calculating future value of an annuity and adjusting for a one-time expense.

The principle of compound interest comes into play, which can be demonstrated by the formula used to calculate the growth of a single investment over time. For instance, a $3,000 investment at a 7% annual rate of return grows to $44,923 over 40 years, illustrating how powerful compound interest can be for early savers. It's advised that saving around 15% of your income can provide a retiree with 60-80 percent of their pre-retirement income. Accumulating significant wealth by retirement is achievable through consistent saving and understanding the impact of interest rates over time.