Kent invested $5,000 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 earn 5% interest per year.
1.Write an expression that represents the amount of money invested in the traditional account.
2.If Kent put $500 in the bond account, how much money does he have in his retirement plan after one year?
Could someone help me on how to solve these two? Thanks
Bonds pay interest semiannually and interest is not compounded.
"Traditional" accounts, like bank savings accounts, pay interest monthly (usually) and add it to the principal.
1. The "traditional account", will have
5000 - X invested in it, initially, if the bond account gets X.
2. The "bond account" would have 500 + 4% or $520 after one year, if X = 500. The Traditional Account, compounded monthly, would have
$4500*(1 + 0.05/12)^12 = $4730.23
1. The amount of money invested in the traditional account can be represented by the expression: $5,000 - X.
2. If Kent put $500 in the bond account, then the amount of money invested in the traditional account would be $5,000 - $500 = $4,500.
To calculate the total amount of money after one year, we need to consider the interest earned. The bond account earns 4% interest per year, and the traditional account earns 5% interest per year.
For the bond account: $500 + ($500 * 4/100) = $500 + $20 = $520
For the traditional account: $4,500 + ($4,500 * 5/100) = $4,500 + $225 = $4,725
Therefore, he would have $520 in the bond account and $4,725 in the traditional account, making a total of $520 + $4,725 = $5,245 in his retirement plan after one year.
Certainly! Let's break down each question step by step.
1. To write an expression representing the amount of money invested in the traditional account, we need to find the difference between the total investment and the amount invested in the bond account.
Let's assume the amount invested in the traditional account is represented by 'T'.
The total investment is $5,000, and we know that $500 is invested in the bond account. Therefore, the amount invested in the traditional account can be found by subtracting the bond amount from the total investment:
T = Total investment - Amount in bond account
Using the numbers given, the expression representing the amount invested in the traditional account would be:
T = $5,000 - $500
T = $4,500
So, the expression representing the amount invested in the traditional account is $4,500.
2. To find the total value of Kent's retirement plan after one year, we need to calculate the interest earned by each account and add it to the initial investment.
The bond account earns 4% interest per year. Kent invested $500 in this account. Therefore, the interest earned in the bond account after one year would be:
Interest on bond account = Amount in bond account * Interest rate
Interest on bond account = $500 * 4% = $20
The traditional account earns 5% interest per year. We found in question 1 that the amount invested in the traditional account is $4,500. Therefore, the interest earned in the traditional account after one year would be:
Interest on traditional account = Amount in traditional account * Interest rate
Interest on traditional account = $4,500 * 5% = $225
To calculate the total value of Kent's retirement plan after one year, we need to add the initial investment and the total interest earned:
Total value after one year = Total investment + Interest on bond account + Interest on traditional account
Total value after one year = $5,000 + $20 + $225
Total value after one year = $5,245
So, after one year, Kent would have $5,245 in his retirement plan.
I hope this helps! Let me know if you have any further questions.