Bertha is investing in a 3-year term investment account. So far she has deposited $1,200 at the beginning of the first year, and $880 at the beginning of the second year. She is planning to deposit another $830 at the beginning of the third year.
Use x=1+r
, where r is the interest rate paid each year. Write a model polynomial, C(x)
, that represents the final amount of Bertha’s investment account.
Find the final amount of Bertha’s investment account if the interest rate is 5.6 percent. Round the answer to two decimal places.
(1 point)
C(x)=
The final amount of Bertha’s investment account if the interest rate is 5.6 percent is $
.
C(x) = (1200)(x^3) + (880)(x^2) + (830)(x)
To find the final amount of Bertha's investment account, we need to substitute x=1+r into the model polynomial and evaluate it for r=0.056 (5.6% in decimal form).
C(1+0.056) = (1200)((1+0.056)^3) + (880)((1+0.056)^2) + (830)(1+0.056)
C(1.056) = (1200)(1.056^3) + (880)(1.056^2) + (830)(1.056)
Evaluating this using a calculator, we get:
C(1.056) ≈ $3208.94
Therefore, the final amount of Bertha's investment account if the interest rate is 5.6 percent is approximately $3208.94.