Question

Kent invested $5000 in a retirement plan. He allocated x dollars of the money to a bond account that earns 4% interest per year and the rest to a traditional account that earns 5% interest per year. A. Write an expression that represents the amount of money invested in the traditional account. B. Write a polynomial model in simplest form for the total amount of money T Kent has invested after one year. (Hint: Each account has A + IA dollars, where A is the original amount in the account and I is its interest rate.) c. If Kent put $500 in the bond account, how much money does he have in his retirement plan after one year?

Answer 1

Answer:  The answers are given below.

Step-by-step explanation:  Given in the question that Kent invested $5000 in a retirement plan. He allocated x dollars of the money to a bond account that earns 4% interest per year and the rest to a traditional account that earns 5% interest per year.

(A) Let, '$y' be the amount of money Kent invested in the traditional account, then we have

$y=5000-x.$

This is the required expression.

(B) After 1 year, total money in the bond account will be

$M_b=x+\dfrac{1\times 4\times x}{100}=x+\dfrac{x}{25}=\dfrac{26}{25}x,$

and amount of money in the traditional account will be

$M_t=(5000-x)+\dfrac{1\times 5\times (5000-x)}{1000}=(5000-x)+\dfrac{5000-x}{200}\\\\\\\Rightarrow M_t=\dfrac{201(5000-x)}{200}.$

Therefore, total amount invested after 1 year will be

$M=M_b+M_t=\dfrac{26}{25}x+\dfrac{201(5000-x)}{200}=\dfrac{208x+1005000-201x}{200}\\\\\\\Rightarrow M=\dfrac{7x+1005000}{200}.$

(C) If x = $500, then we have

$M=\dfrac{7\times 500+1005000}{200}=\dfrac{1008500}{200}=\dfrac{10085}{2}=5042.5.$

Thus, Kent will have $5042.5 in his retirement plan after 1 year.