Kevin takes out a 10-year loan of l, which he repays by the amortization method at an annual effective interest rate of i. kevin makes payments of 1000 at the end of each year. the total amount of interest repaid during the life of the loan is also equal to l. calculate the amount of interest repaid during the first year of the loan.

first year interest paid: 754.92 dollars

Explanation:

Kevin makes 10 payment of 1,000 dollars

This pays interest and principal

we know that principal is L and total interest is also L

so: principal = total interest

10,000 = principal + total interest

10,000 = 2L

L = 5,000

the principal is 5,000 and the interest are 5,000

To know the interest in the first period we need to solve for rate of a 10 years annuity of 1,000:

This is solve with financial calculator or excel using "goal seek" in the Data pannel.

This will give us: 0.150984145

Now, we calcualte the interest for the first year:

principal x rate

5,000 x 0.150984145 = 754.920726 = 754.92 dolllars

a) NH₄NO₃ ⇒ N₂O + 2 H₂O

b) 1.69 × 10²³ molecules

Explanation:

Step 1: Write the balanced equation

NH₄NO₃ ⇒ N₂O + 2 H₂O

Step 2: Convert 11.2 g of NH₄NO₃ to moles

The molar mass of NH₄NO₃ is 80.04 g/mol.

11.2 g × 1 mol/80.04 g = 0.140 mol

Step 3: Calculate the moles of H₂O produced

0.140 mol NH₄NO₃ × 2 mol H₂O/1 mol NH₄NO₃ = 0.280 mol H₂O

Step 4: Calculate the number of molecules in 0.280 moles of water

We will use Avogadro's number.

0.280 mol × 6.02 × 10²³ molecules/1 mol = 1.69 × 10²³ molecules