Question

Two accounts earn simple interest. The balance y (in dollars) of an Account A after X years can be modeled by y=30x+500. Account B starts with $450 and earns 2% simple annual interest. Which account has a greater principal? How much greater is the principal? Which account has a greater interest rate? How much greater is the annual interest rate?

Answer 1

1) Account A has a greater principal

2)Principal in Account A is greater than principal in account B by $50.

3)Account A has greater interest rate

4) interest rates in Account A is greater than interest rate in account B by 4%

Explanation:

We are told that amount left in account A after X years is; y = 30x + 500

Now,amount left after X number of years in simple interest is given by the formula;

A = P(1 + rt)

Where;

P is principal

r is interest rate

t is time

Thus, rewriting the model equation given to depict this form, we have;

y = 30x + 500 = 500(1 + (30/500)x) =

Comparing with the simple interest formula, we have;

P = $500

r = 30/500 = 0.06 = 6%

t = x

Now, in account B, we have;

Principal; P = $450

Interest rate; r = 2% = 0.02

1) From above 2 accounts we can see that Account A has a greater principal

2) Difference in principal = $500 - $450 = $50. Principal in Account A is greater than principal in account B by $50.

3) Account A has greater interest rate

4) Difference in annual interest rate = 6% - 2% = 4%. Thus, interest rates in Account A is greater than interest rate in account B by 4%