How much more would you earn in the first investment than in the second investment?$25,000 invested for 50 years at 14% compounded annually$25,000 invested for 50 years at 7% compounded annually You would earn how many dollars more on the first investment than in the second investment. Round to the nearest dollar as needed.

To determine how much more you would earn on the first investment compared to the second, we'll use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money after interest,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate,
- $ n $ is the number of times the interest is compounded per year (for annual compounding, $ n = 1 $),
- $ t $ is the number of years.

Let's calculate the final amounts for both investments:

1. **First Investment:**
   - Principal $ P = 25,000 $,
   - Interest rate $ r = 14\% = 0.14 $,
   - Time $ t = 50 $ years,
   - Compounding annually ($ n = 1 $).

\[
A_1 = 25,000 \left(1 + \frac{0.14}{1}\right)^{1 \times 50} = 25,000 \times (1.14)^{50}
\]

2. **Second Investment:**
   - Principal $ P = 25,000 $,
   - Interest rate $ r = 7\% = 0.07 $,
   - Time $ t = 50 $ years,
   - Compounding annually ($ n = 1 $).

\[
A_2 = 25,000 \left(1 + \frac{0.07}{1}\right)^{1 \times 50} = 25,000 \times (1.07)^{50}
\]

I’ll now calculate both results and determine how much more you earn on the first investment than the second.The amount after 50 years for the first investment at 14% is $17,505,825, and for the second investment at 7%, it is $736,426. The difference in earnings between the two investments is **$16,769,399**.

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How would the earnings change if the compounding frequency increased to semi-annual or quarterly?
2. What is the total interest earned on each investment separately?
3. How does changing the interest rate by just 1% affect the total earnings over 50 years?
4. What happens if the investments are made for a shorter period, like 30 years, with the same interest rates?
5. How does compounding affect your returns compared to simple interest?

**Tip**: Compounding is powerful, especially over long periods. The higher the rate and the longer you leave the investment, the more exponential the growth.

How much more would you earn in the first investment than in the second investment? $25,000 invested for 50 years at 14% compounded annually vs $25,000 invested for 50 years at 7% compounded annually. You would earn how many dollars more on the first investment than in the second investment. Round to the nearest dollar as needed.

Find out how much more you would earn with $25,000 invested for 50 years at 14% compounded annually compared to 7%. This detailed solution explains the compound interest formula and demonstrates how the exponential growth of investments works over time.

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