Discrete Math Chapter 8 - Pretest. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Discrete Math Name Chapter 8 - Pretest Date SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Round answer to the nearest cent. 1) P = $140 1) r = 3% t = 4 years 2) P = $400 r = 7.75% t = 3 months 2) The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. Round answer to the nearest cent. 3) P = $110 3) r = 7% t = 2 years 4) P = $7500 r = 8.5% t = 16 months 4) The principle represents an amount of money deposited in a savings account subject to compound interest at the rate shown. Find how much money will be in the account after the given number of years and how much interest was earned in that period. 5) principal: $5000 5) rate: 4% compounding periods per year: 1 time: 3 years 6) principal: $5500 rate: 5.5% compounding periods per year: 12 time: 5 years 6) Solve the problem. 7) If you placed $1 into an account that paid interest at a rate of 6% and compounded the interest daily, how much would that account be worth in 300 years? 7) 1

2 8) A mother invests $3000 in a bank account at the time of her daughter's birth. The interest is compounded quarterly at a rate of 12%. What will be the value of the daughter's account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period? 8) 9) Which is the better choice: $1000 deposited for a year at a rate of 4.7% compounded quarterly or at a rate of 4.6% compounded monthly? 9) 10) Suppose Carla has $13,000 to invest. Which investment yields the greater return over 4 years: 10% compounded semiannually or 9.85% compounded quarterly? 10) 11) How much money should be deposited today in an account that earns 5% compounded semiannually so that it will accumulate to $8000 in 11 years? 11) 12) How much money should be deposited today in an account that earns 11% compounded quarterly so that it will accumulate to $8600 in 12 years? 12) 13) James and Susan wish to have $10,000 available for their wedding in 3 years. How much money should they set aside now at 18% compounded monthly in order to reach their financial goal? 13) 14) A passbook savings account has a rate of 7.6%. Find the effective annual yield if the interest is compounded quarterly. 14) 2

3 15) A passbook savings account has a rate of 5%. Find the effective annual yield if the interest is compounded 10,000 times per year. 15) 16) You have a choice of two accounts in which to invest your money for one year. Account A pays 7.7% simple interest rate and account B pays 6.5% interest compounded daily. Compute the effective annual yield of account B and determine which account has the better rate. (Assume that there are 360 days in a year.) 16) Find the value of the annuity. 17) Periodic Deposit Rate Time $1000 at the end of each year 6% compounded annually 13 years 17) 18) Periodic Deposit Rate Time $7500 at the end of every six months 5% compounded semiannually 2 years 18) Determine the periodic deposit for the annuity. 19) Periodic Deposit Rate Time Financial Goal $? at the end of each month 18% compounded monthly 3 years $46,000 19) 20) Periodic Deposit Rate Time Financial Goal $? at the end of every three months12% compounded quarterly 5 years $26,000 20) Solve the problem. Round answers to the nearest dollar. 21) The cost of a boat is $29,000. Arthur finances this by paying $6000 down and $ per month for 36 months. Determine a. the amount financed; b. the total installment price; c. the finance charge. 21) 3

4 22) A particular credit card calculates interest using the unpaid balance method. The monthly interest rate is 1.37% on the unpaid balance on the first day of the billing period less payments and credits. Here are some of the details in the July 1 - July 31 itemized billing: July 1 Unpaid Balance: $1412 Payment Received July 10: $300 Purchases Charged to the VISA Account: meals, $88; theater tickets, $49; computer accessories, $380 Last Day of the Billing Period: July 31 Payment Due Date: August 9 a. Find the interest due on the payment due date. b. Find the total balance owed on the last day of the billing period. c. This credit card requires a $10 minimum monthly payment if the total balance owed on the last day of the billing period is less than $360. Otherwise, the minimum monthly payment is 1/36 of the balance owed on the last day of the billing period, rounded to the nearest whole dollar. What is the minimum monthly payment due by August 9. 22) Solve the problem. 23) On the August 28 billing date, Marcus had a balance due of $ on his credit card. The transactions during the following month were: August 30 Payment $ September 2 Charge: camcorder $ September 8 Charge: bicycle $ September 21 Charge: shoes $51.97 The interest rate on the card is 1.5% per month. Using the unpaid balance method, find the new balance on September ) 24) On the July 5 billing date, David had a balance due of $ on his credit card. The transactions during the following month were: July 6 Payment $ July 19 Charge: auto repair $322 August 1 Charge: clothing $ The interest rate on the card is 1.2% per month. Using the average daily balance method, find the finance charge on August 5 (July has 31 days). 24) 4

5 25) The price of a home is $380,000. The bank requires a 10% down payment and one point at the time of closing. The cost of the home is financed with a 25-year fixed-rate mortgage at 6.5%. a. Find the required down payment. b. Find the amount of the mortgage. c. How much must be paid for the one point at closing? d. Find the total cost of interest over 25 years, to the nearest whole dollar. 25) 26) In terms of paying less in interest over the full term of the mortgage, which is more economical for a $300,000 mortgage : 25-year fixed at 8.00% or 15-year fixed at 7.50%? 26) 27) The price of a home is $330,000. The bank requires a 5% down payment. After the down payment, the balance is financed with a 30-year fixed-rate mortgage at 8.5%. Determine the monthly mortgage payment (excluding escrowed taxes and insurance) to the nearest dollar. 27) 28) A real estate company borrowed $385,000 to develop some condos. It amortized the loan to pay monthly for 4 years at 12% interest. Find the amount of each monthly payment. 28) 29) Prepare a loan amortization schedule for the first three months of the following mortgage loan. 29) AMORTIZATION SCHEDULE Annual % rate: 7% Amount of Mortgage: $280,000 Monthly payment: $ Term: Years 30, Months 0 Number of Monthly Payments: 360 Payment Number Interest Payment Principal Payment Balance of Loan 5

6 30) A new fax machine cost Miller Ltd. $2944. They are to pay it off in 18 months at 18% interest. What will each monthly payment be, and how much interest will they pay on the loan? 30) 31) The cost of a home on a particular island is $1,000,000. The bank requires a 15% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed rate at 8%. Find: 31) a. the required down payment b. the amount of the mortgage c. the amount that must be paid for the three points at closing d. the monthly payment e. the total cost of interest over 30 years. 6

7 Answer Key Testname: CH8PRTST 1) $ ) $7.75 3) $ ) $ ) amount in account: $ ; interest earned: $ ) amount in account: $ ; interest earned: $ ) $65,561, ) $31, ) The rate of 4.7% compounded quarterly is better. 10) The rate of 10% compounded semiannually is better. 11) $ ) $ ) $ ) 7.8% 15) 5.13% 16) Account A 17) $18, ) $31, ) $ ) $ ) a. amount financed: $23,000; b. total installment price: $34,520; c. finance charge: $ ) a. $15.23 b. $ c. $46 23) $ ) $ ) a. down payment: $38,000 b. amount of mortgage: $342,000 c. points paid at closing: $3420 d. total cost of interest over 25 years: $350,550 26) The 15-year fixed rate at at 7.50% is more economical. 27) $ ) $10, ) Payment Interest Principal Balance Number Payment Payment of Loan , , , ) $187.84, $ ) a. $150,000; b. $850,000; c. $25,500; d. $6237; e. $1,395,320 7