Texas Go Math Grade 8 Lesson 16.2 Answer Key Saving and Investing

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Texas Go Math Grade 8 Lesson 16.2 Answer Key Saving and Investing

Texas Go Math Grade 8 Lesson 16.2 Explore Activity Answer Key

Explore Activity 1

Calculating Simple Interest

Interest is money paid by banks and others for the use of depositors’ money. Simple interest is earned using the formula l = Prt, where l is the amount of interest, P is the principal, or the original amount deposited, r is the interest rate expressed as a decimal, and f is the time in years. Simple interest is paid at the end of the term based only on the principal at the beginning.

Adan makes regular deposits to a savings account to save money for college. He deposits $1000 at the start of each year into an account that pays 4% simple interest at the end of each year. He does not deposit the interest.

A. How much interest does Adan’s account earn the first year?
l = Prt Use the formula for simple interest.
l = 1000 × __________ × 1 = __________ Substitute and simplify
Adan’s account earns ___________ the first year.

B. Complete the table to show how the interest earned grows over time.
Texas Go Math Grade 8 Lesson 16.2 Answer Key 1

Reflect

Question 1.
How much interest did Adan’s account earn from the initial deposit to the end of year 5? from the start of year 6 to the end of year 10? How do these values compare? Explain.
Answer:

Question 2.
What was the total amount saved from the initial deposit to the end of year 5? from the start of year 6 to the end of year 10? Include the amount contributed and the interest.
Answer:

Explore Activity 2

Calculating Compound interest

Compound interest is interest paid not only on the principal but also on any interest that has already been earned. Every time interest is calculated, the interest is added to the principal for future interest calculations. The calculation can be made more than once a year, but in this lesson only interest compounded annually will be found.

The formula for compound interest is A = P(1 + r)t, where P is the principal, r is the interest rate expressed as a decimal, t is the time in years, and A is the amount in the account after t years if no withdrawals were made.

Lilly makes regular deposits to a savings account to save money for retirement. She deposits $1000 each year, and her account earns interest compounded annually at a rate of 4%.
A. How much interest does Lilly earn the first year?
A = P(1 + r)t Use the formula for compound interest.
A = 1000 × (1 + __________) 1 Substitute
A = _________ Simplify
So, Lilly’s account earns __________ – $1000 = __________ the first year.

B. Complete the table to show how the amount in the account accumulates over time. Round all values to the nearest cent.
Texas Go Math Grade 8 Lesson 16.2 Answer Key 2

Reflect

Question 3.
How much interest did Lilly’s account earn from the initial deposit to the end of year 5? from the start of year 6 to the end of year 10?
Answer:

Question 4.
Compare the interest earned during the two five-year periods. Explain the difference.
Answer:

Question 5.
Compare the final balance in this Explore Activity to the total amount deposited and earned in interest in Explore Activity 1 (see Reflect question 2). What can you conclude?
Answer:

Your Turn

Question 6.
Marlena saved $50 in an account earning 3.5% simple interest. How much more interest would her account earn in 10 years if her account earned interest compounded annually instead of simple interest?
Answer:

Texas Go Math Grade 8 Lesson 16.2 Independent Practice Answer Key

Question 1.
Gina deposits $150 at the start of each year into a college savings account that pays 4% simple interest at the end of each year. She does not deposit the interest she earns each year. How much total interest will Gina earn on her deposits through the end of the fifth year? (Explore Activity 1)
Answer:

Question 2.
Fredo deposits $75 each year in an account earning 3% interest compounded annually. If he deposits an additional $75 per year and does not make any withdrawals, how much interest will the account earn in the fourth year? (Explore Activity 2)
Answer:

Question 3.
Huan deposited $850 into a college savings account earning 4.8% interest compounded annually. He also deposited $850 into a second account earning 4.8% simple interest. He made no additional deposits. (Example 1)
a. How much interest does the first account earn in 10 years?
Answer:

b. How much interest does the second account earn in 10 years?
Answer:

c. After 10 years, which account earned more interest? How much more?
Answer:

Question 4.
Andreas invested $1000 in a savings account. After 4 years, the account had earned a total of $112 simple interest without any additional deposits. What was his interest rate?
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Question 5.
Hei has $1500 in a retirement account earning 5% interest compounded annually. Each year after the first, she makes additional deposits of $1500. After 5 years, what was her account balance if she did not make any withdrawals?
Answer:

Question 6.
Lester deposited $400 into a savings account earning 4.5% simple interest, and $450 into an investment account earning 3.2% interest compounded annually. What was the total interest he earned in 3 years? Justify your reasoning.
Answer:

Question 7.
Randee invested $1000 for college in an account earning 5% simple interest. When she withdrew the investment, she had earned a total of $550 in interest. How long was the money invested? Justify your reasoning.
Answer:

Question 8.
Critical Thinking Is it possible for an amount of money invested in an account earning simple interest to earn more interest than the same amount of money invested at the same rate in an account earning interest compounded annually? Explain.
Answer:

H.O.T. Focus on Higher Order Thinking

Question 9.
Multiple Representations The graph shows how the values of two accounts increase over time. The line represents $50 invested in an account paying 5% simple interest, and the curve represents $50 invested in an account paying 5% interest compounded annually. Write an equation for the line and for the curve. Assume no additional deposits were made to either account.
Texas Go Math Grade 8 Lesson 16.2 Answer Key 3
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Question 10.
Critique Reasoning Marco says he will earn more interest on his $100 savings if he gets 4% interest compounded annually than if he gets 5% simple interest. How many years does he have to keep the money in the bank without withdrawing any to be right? Justify your reasoning.
Answer:

Question 11.
Critique Reasoning Parker invested $6,500 for 2 years, part at 6% interest compounded annually and part at 5% simple interest. He earned three times as much interest in the account paying compound interest as in the account paying simple interest. Can Parker model this situation using the equation x(1 + 0.06)2 = 3(6500 – x)(0.05)(2), where x is the initial amount in the 6% account and 6500 – x is the amount in the 5% account? Explain.
Answer:

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