# Mathematics

**MATH 105 Final Exam**

Maria and John have been married for 2 years and just learned that they are pregnant.

1. They have been renting a small apartment but decide to purchase a house.

They find one that is selling for $400,000. They decide to make a 20% down payment on a 30-year mortgage at 3.75%.

Answer each of the following questions separately, showing all your work to reach each answer.

a. How much will they need for the **down paym**ent?

b. What will be the **mortgage amount** (ie the principal)

c. How much will their **monthly payment** be for the principal and interest?

d. How much **total interest** will they pay if they take the full 30 years to pay off the mortgage?

2. They decide to shop for the new house. They choose items that amount to $ 1800.00. The store has 2 options for purchasing:

I. financing at 6% simple interest per year for 2 years with a 10% down payment.

II. no down payment and financing at 5.2% simple interest for 3 years.

Answer each of the following questions separately, showing all your work to reach each answer.

a. Which option should they choose if they want the smallest **finance charge?**

b. Which option should they choose if they want the smallest total **installment price**?

c. Which option should they choose if they want the smallest **amount of the monthly payment**?

3. Maria’s parents tell them that they will set up a savings account for their first grandchild. They have $10,000to invest and have identified an account that pays 3% compounded weekly.Since Maria and John both just finished a course on consumer mathematics, they each decide to calculate how much interest will have been earned at the end of 10 years and the end of 18 years.

Maria is very precise and never rounds her decimal places until the end of her calculations.

John always rounds each intermediate step to 5 decimal places.

Answer each of the following questions separately, showing all your work to reach each answer.

a. How much interest will Maria calculate for each time period (10 years and 18 years)?

b. How much interest will John calculate for each time period? (10 years and 18 years)?

4. Maria and John decide to save for retirement with an annuity.

Answer each of the following questions separately, showing all your work to reach each answer.

a. Maria has found an **annuity**that pays 2% compounded monthly. If they made a deposit of $200 each month, what would be the **total value** of this annuity at the end of 30 years if interest rate remains the same?

b. John has found an **annuity**that pays 2.5% compounded semi-annually. If they made a deposit of $1000 every six months, what would be the **total value** of this annuity at the end of 30 years if interest rate remains the same?

5. Maria and John have decided that once they live in a home, they want to have a pet. Maria prefers cats and John prefers dogs. They go to an animal shelter and find several pets that they would love to take home. There are 7 Siamese cats, 9 common cats, 4 German Shepherds, 2 Labrador Retrievers, and 6 mixed-breed dogs. Since they can’t decide, they place all the adoption cards in a container and draw one.

Answer each of the following questions separately, showing all your work to reach each answer.

a. What is the probability that they select a cat?

b. What are the **odds** that they select a cat?

c. What is the probability that they select **either **a common cat **or** a mixed-breed dog?

d. What is the probability that they select a dog that it is **not** a Labrador Retriever?