To determine which bank will yield a higher return for Jelly Roll's investment after 5 years, we can calculate the future value of the investment with both JP Morgan and Chase.
1. JP Morgan: Compounded Semi-Annually at 5%
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the future value of the investment/loan, including interest
- \( P \) = the principal investment amount ($1,499,000)
- \( r \) = the annual interest rate (decimal) (5% = 0.05)
- \( n \) = the number of times that interest is compounded per year (2 for semi-annual)
- \( t \) = the number of years the money is invested or borrowed (5)
Substituting in the values for JP Morgan:
\[ A = 1,499,000 \left(1 + \frac{0.05}{2}\right)^{2 \times 5} \] \[ A = 1,499,000 \left(1 + 0.025\right)^{10} \] \[ A = 1,499,000 \left(1.025\right)^{10} \] \[ A \approx 1,499,000 \times 1.280084 \] \[ A \approx 1,915,649.08 \]
2. Chase: Compounded Annually at 5.2%
Using the same compound interest formula:
Substituting in the values for Chase:
\[ A = 1,499,000 \left(1 + \frac{0.052}{1}\right)^{1 \times 5} \] \[ A = 1,499,000 \left(1 + 0.052\right)^{5} \] \[ A = 1,499,000 \left(1.052\right)^{5} \] \[ A \approx 1,499,000 \times 1.288634 \] \[ A \approx 1,932,877.065 \]
Final Calculations:
- JP Morgan Amount: \( \approx 1,915,649.08 \)
- Chase Amount: \( \approx 1,932,877.065 \)
Conclusion:
After 5 years, Jelly Roll will have approximately:
- JP Morgan: $1,915,649.08
- Chase: $1,932,877.065
Thus, Chase offers a higher return after 5 years. The corrected calculations indicate an error in the options provided, but based on our calculations, Chase will result in more money.
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