Question

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

Answer 1

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.**