Interest, Sequences, and Financial Applications Quiz

What is the fundamental difference between simple interest and compound interest? Explain in your own words.

• Simple interest can be reinvested to earn more interest.
• Compound interest is calculated only on the principal amount.
• The fundamental difference is that simple interest is calculated only on the principal, whereas compound interest is calculated on the principal plus accumulated interest.
• Simple interest is always higher than compound interest.

If you deposit $500 into an account that earns 3% simple interest annually, how much interest will you have earned after 5 years?

• $75
• $60

• $70

• $65

Suppose you invest $1000 in an account that pays 5% interest compounded annually. How much will you have in the account after 3 years?

• $1157.63
• $1158.38

• $1345.53

• $1256.23

Explain how the frequency of compounding (e.g., annually, semi-annually, quarterly, monthly) affects the total interest earned on an investment. Give an example.

• More frequent compounding decreases the total interest earned.
• Compounding has no effect on the total interest earned.
• Annual compounding is always better than monthly compounding.
• More frequent compounding increases the total interest earned on an investment.

What is the future value of $2000 invested at 4% interest compounded quarterly for 4 years?

• $2348.64
• $3243.32

• $1234.54

• $5432.12

What is the present value of $5000 you need in 5 years if the interest rate is 6% compounded annually?

• $3736.29
• $3740.30

• $3830.25

• $3645.35

Define APR and APY. Explain why APY is usually higher than APR.

• APR is the annual cost of borrowing without compounding; APY includes compounding, making it usually higher.
• APY is calculated without considering compounding; APR includes compounding effects.
• APR is the total interest paid over the loan term; APY is the interest rate for a single period.
• APR is always higher than APY because it reflects total costs of borrowing.

You are considering two savings accounts. Account A offers 4.5% APR compounded monthly, and Account B offers 4.4% APR compounded daily. Which account would yield a higher return after one year? Why?

• Account B yields a higher return after one year.
• Account A yields a higher return after one year.
• Both accounts yield the same return after one year.
• Account A yields a lower return after one year.

Define an arithmetic sequence. What is the key characteristic that distinguishes it from other types of sequences?

• An arithmetic sequence has a constant difference between consecutive terms.
• An arithmetic sequence is defined by a geometric ratio between terms.
• An arithmetic sequence consists of random numbers without any specific pattern.
• An arithmetic sequence has a variable difference between terms.

Which of the following sequences are arithmetic? Explain your reasoning. a) 2, 4, 8, 16, … b) 1, 5, 9, 13, … c) 10, 7, 4, 1, …

• 2, 4, 6, 8, ...
• 5, 10, 15, 20, ...
• 3, 6, 9, 12, ...
• b) and c) are arithmetic sequences.

  • a) Not arithmetic (multiplicative pattern), b) Arithmetic (difference of 4), c) Arithmetic (difference of -3)