Jelly Roll wants to invest the $1,499,000 that he made at his last concert in an account. His final decision is between JP Morgan and Chase. JP Morgan offers a 5% interest rate compounded semi-annually. Chase offers a 5.2% interest rate compounded annually. Where will he make more money if he leaves his money invested for 5 years?

JP Morgan; $1918846.73

JP Morgan; $1931436.04

Chase; $1918846.73

Chase: $1931436.04

1 answer

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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