## Engage NY Eureka Math Algebra 1 Module 3 Lesson 4 Answer Key

### Eureka Math Algebra 1 Module 3 Lesson 4 Example Answer Key

Example 1.

Kyra has been babysitting since sixth grade. She has saved $1,000 and wants to open an account at the bank so that she earns interest on her savings. Simple Bank pays simple interest at a rate of 10%. How much money will Kyra have after 1 year? After 2 years, if she does not add money to her account? After 5 years?

Answer:

$1,100 after 1 year, $1,200 after 2 years, $1,500 after 5 years

Raoul needs $200 to start a snow cone stand for this hot summer. He borrows the money from a bank that charges 4% simple interest per year.

a. How much will he owe if he waits 1 year to pay back the loan? If he waits 2 years? 3 years? 4 years? 5 years?

Answer:

$208, $216, $224, $232, $240

b. Write a formula for how much he will owe after t years.

Answer:

A(t) = 200+200(0.04)t

Example 2.

Jack has $500 to invest. The bank offers an interest rate of 6% compounded annually. How much money will Jack have after 1 year? 2 years? 5 years? 10 years?

Answer:

$530, $561.80, $669.11, $895.42

Example 3.

If you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or in a bank that pays 5% interest compounded annually? Is there anything you could change in the problem that would make you change your answer?

Answer:

7% for 10 years gives $140 in simple interest, or $340 total.

5% compounded for 10 years gives $325.78.

### Eureka Math Algebra 1 Module 3 Lesson 4 Problem Set Answer Key

Question 1.

$250 is invested at a bank that pays 7% simple interest. Calculate the amount of money in the account after 1 year, 3 years, 7 years, and 20 years.

Answer:

$267.50, $302.50, $372.50, $600.00

Question 2.

$325 is borrowed from a bank that charges 4% interest compounded annually. How much is owed after 1 year, 3 years, 7 years, 20 years?

Answer:

$338.00, $365.58, $427.68, $712.12

Question 3.

Joseph has $10,000 to invest. He can go to Yankee Bank that pays 5% simple interest or Met Bank that pays 4% interest compounded annually. At how many years will Met Bank be the better choice?

Answer:

At 12 years, Met Bank is a better choice.

### Eureka Math Algebra 1 Module 3 Lesson 4 Exit Ticket Answer Key

Question 1.

A youth group has a yard sale to raise money for a charity. The group earns $800 but decides to put its money in the bank for a while. Calculate the amount of money the group will have given the following scenarios:

a. Cool Bank pays simple interest at a rate of 4%, and the youth group leaves the money in for 3 years.

Answer:

$800(0.04)(3) = $96 interest earned

$896 total

b. Hot Bank pays an interest rate of 3% compounded annually, and the youth group leaves the money in for 5 years.

Answer:

$800(1.03)^{5} = $927.42

c. If the youth group needs the money quickly, which is the better choice? Why?

Answer:

If the youth group needs the money quickly, it should use Cool Bank since that bank pays a higher rate than Hot Bank. The lower rate is better for a longer period of time due to the compounding interest.