Final answer:
In this case, you would earn approximately $4,092,676.51 more on the first investment than in the second investment.
Step-by-step explanation:
To calculate how much more you would earn in the first investment than in the second investment, we need to use the compound interest formula and compare the final balances.
For the first investment, we have:
Principal (P) = $49,000
Interest rate (r) = 10% = 0.10
Number of years (t) = 50
Compounding periods per year (n) = 1 (compounded annually)
Using the formula A = P(1 + r/n)⁽ⁿᵗ⁾, we can calculate the final balance:
A = $49,000 * (1 + 0.10/1)⁽¹*⁵⁰⁾
A ≈ $4,524,871.45
For the second investment, we have:
Principal (P) = $49,000
Interest rate (r) = 5% = 0.05
Number of years (t) = 50
Compounding periods per year (n) = 12 (compounded monthly)
Using the same formula, we can calculate the final balance:
A = $49,000 * (1 + 0.05/12)⁽¹²*⁵⁰⁾
A ≈ $432,194.94
To find the difference between the two investments, we subtract the final balance of the second investment from the final balance of the first investment:
Difference = $4,524,871.45 - $432,194.94
Difference ≈ $4,092,676.51
Therefore, you would earn approximately $4,092,676.51 more on the first investment than in the second investment.
Your question is incomplete, but most probably the full question was:
How much more would you earn in the first investment than in the second investment? $49,000 invested for 50 years at 10% compounded annually $49,000 invested for 50 years at 5% compounded monthly Click the icon to view some finance formulas. You would earn ...$ more on the first investment than in the second investment. (Round to the nearest dollar as needed.)
Formulas
A = P(1 + (n * r) / n)⁽ⁿ * ᵗ⁾
Y = (1 + (n * r) / n)⁽¹/ⁿ⁾ ⁻ ¹
In the provided formulas, A is the balance in the account after t years, P is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and Y is the investment's effective annual yield in decimal form.