To calculate the interest earned at the end of the 9-year term, we need to subtract the initial deposit from the final value of the investment.
Using the given equation C(x) = 350x^9 + 500x^5 + 820x, where x = 1 + r (annual interest rate), we substitute x = 1 + 1.75% = 1.0175 into the equation:
C(1.0175) = 350(1.0175)^9 + 500(1.0175)^5 + 820(1.0175)
C(1.0175) = 350(1.172245965) + 500(1.089630963) + 820(1.0175)
C(1.0175) = 411.2850838 + 544.8154815 + 834.95
C(1.0175) = 1791.0505653
To calculate the interest earned, we subtract the initial deposit of $350 from the final value:
Interest earned = Final value - Initial deposit
Interest earned = 1791.0505653 - 350
Interest earned = $1441.0505653
Rounded to the nearest cent, the interest earned at the end of the 9-year term is $1441.05. None of the given answer choices match this amount, so the correct answer is none of the above.
Consider an investment account with a 9-year term. The amounts of $350, $500, and $820 were deposited into the account at the beginning of the first, fifth, and ninth years, respectively. The equation C(x)=350x^9+500x^5+820x represents the relationship between C(x) , the value of an investment account with a 9-year term, and its annual interest rate, r, where x=1+r . How much interest is earned at the end of the 9-year term if the annual interest rate is 1.75%?(1 point)
1. $1,670.00
2. $1,907.55
3. $1,788.80
4. $118.30
1 answer