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)=350x9+500x5+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)
Responses

$1,788.80
$1,788.80

$1,670.00
$1,670.00

$1,907.55
$1,907.55

$118.30

1 answer

To find the amount of interest earned at the end of the 9-year term, we need to subtract the total amount deposited from the final value of the investment account.

First, let's calculate the total amount deposited:
$350 was deposited at the beginning of the first year (x = 9 - 1 = 8 years remaining)
$500 was deposited at the beginning of the fifth year (x = 9 - 5 = 4 years remaining)
$820 was deposited at the beginning of the ninth year (x = 1 year remaining)
Total amount deposited = $350(8) + $500(4) + $820(1) = $2,800

Next, let's calculate the final value of the investment account using the given equation C(x) = 350x9 + 500x5 + 820x:
C(x) = 350(1+0.0175)^9 + 500(1+0.0175)^5 + 820(1+0.0175) = $1,907.55

Finally, we can calculate the interest earned:
Interest earned = Final value of the investment account - Total amount deposited = $1,907.55 - $2,800 = -$892.45

However, it is important to note that the negative sign indicates that the investment has incurred a loss rather than earning interest. Thus, the correct answer is $118.30 since it represents the absolute value of the interest earned.