Answer:
Face value of the CD = $1350
S&P 500 index at maturity = $1500
Percentage of gain on the S&P 500 index = 80%
To calculate the gain on the S&P 500 index, we find the difference between the index value at maturity and the face value of the CD:
Gain on the S&P 500 index = S&P 500 index at maturity - Face value of the CD
Gain on the S&P 500 index = $1500 - $1350
Gain on the S&P 500 index = $150
The total payoff from the CD is the sum of the face value and 80% of the gain on the S&P 500 index:
Total payoff = Face value + (Percentage of gain * Gain on the S&P 500 index)
Total payoff = $1350 + (0.80 * $150)
Total payoff = $1350 + $120
Total payoff = $1470
Therefore, the total payoff from the CD when it matures in 3 years and the S&P 500 index goes up to $1500 would be $1470.