Earnings Comparison of Two Investments

How much more would you earn in the first investment than in the second​ investment? ​$22 comma 000 invested for 50 years at 12​% compounded annually ​$22 comma 000 invested for 50 years at 6​% compounded annually LOADING... Click the icon to view some finance formulas. Question content area bottom Part 1 You would earn ​$    more on the first investment than in the second investment. ​(Round to the nearest dollar as​ needed.)

To find out how much more you would earn in the first investment than in the second investment, we can use the formula for compound interest:

[ A = P(1 + r)^n ]

Where:

• ( A ) is the amount of money accumulated after n years, including interest.
• ( P ) is the principal amount (the initial amount of money).
• ( r ) is the annual interest rate (decimal).
• ( n ) is the number of years the money is invested or borrowed.

First Investment:

• ( P = 22,000 )
• ( r = 0.12 ) (12%)
• ( n = 50 )

Calculating the amount for the first investment:

[ A_1 = 22000(1 + 0.12)^{50} ]

Calculating ( (1 + 0.12)^{50} ):

[ (1.12)^{50} \approx 289.256 ]

Now, calculate ( A_1 ):

[ A_1 \approx 22000 \times 289.256 \approx 6,358,632 ]

Second Investment:

• ( P = 22,000 )
• ( r = 0.06 ) (6%)
• ( n = 50 )

Calculating the amount for the second investment:

[ A_2 = 22000(1 + 0.06)^{50} ]

Calculating ( (1 + 0.06)^{50} ):

[ (1.06)^{50} \approx 18.679 ]

Now, calculate ( A_2 ):

[ A_2 \approx 22000 \times 18.679 \approx 410,938 ]

Difference in Earnings:

Now, we find the difference between the two investments:

[ \text{Difference} = A_1 - A_2 ]

[ \text{Difference} \approx 6,358,632 - 410,938 \approx 5,947,694 ]

Final Answer:

You would earn approximately $5,947,694 more on the first investment than on the