Math 107 Test 1 Study Guide 4A-4D

4A: (27) Prorate the following expenses and find the corresponding (Monthly) expenses. Question: Lan pays a semiannual premium of $650 for automobile insurance, a monthly premium of $125 for health insurance, and an annual premium of $400 for life insurance.

$650*2(Semi is two)=$1300 Auto Insurance. $125*12(Monthly is twelve)=$1500 Health Insurance $400(annual is one) $1300+$1500+$400=$3200/12=$266.67

4A: (15) Compute the total cost per year of the following pairs of expenses. Then complete the sentence: On an annual basis, the first set of expenses is ______% of the second set of expenses. Question: Suzanne's cell phone bill is $85 per month, and she spends $200 per year on student health insurance.

$85*(12 months in a year)=$1020 $200 per year $1020/200=5.1*100=510%

4B: (55) Do yourself.

...

4B (53) Calculate the amount of money you will have in the following accounts after 5 years, assuming that you earn simple interest. You deposit $3200 in an account with an annual interest rate of 3.5%

0.035*$3200=$112 5(years)*$112=$560(Interest) Total Balance: $3200=$560=$3760

4A: (24) Find the monthly interest payments in the following situations. Assume that monthly interest rates are 1/12 of annual interest rates. Question: Deanna owes a clothing store $700, but until she makes a payment, she pays 9% interest per month.

0.09*$700=$63

4B: (24) 6^(2)x6^(-2)

1

4B: (18) 3^-2

1/3^2=1/3*3=1/9

4B: (21) 64^-1/3

1/4

4C (29) Total and Annual returns. Compute the total and annual returns on the following investments. Five years after buying 100 shares of xyz stock for $60 per share

100*60=6,000 9400-6000/6000=0.566666667*100=56.7% (9400/6000)^(1/5)-1=0.093944579*100=9.4%

4C: (27) Suppose you are 30 years old and would like to retire at age 60. Furthermore, you would like to have a retirement fund from which you can draw an income of $100,000 per year forever! Assume an APR of 6%

100,000/0.06=1666666.667 1666666.667*(0.06/12)/[(1+0.06/12)^(12x30)-1] =$1,659.18

4C: Bond yields. Compute the current yield on the following bonds. A $1000 Treasury bond with a coupon rate of 2.0% that has a market value of $950

1000*0.02=20 20/950=0.021052632*100=2.11%

4B: (87) How much must you deposit today into the following accounts in order to have a $120,000 college fund in 15 years? An APR of 2.8%, compounded quarterly

120,000/(1+0.028/4)^(4*15) $78,961.07

4B: (85) How much must you deposit today into the following accounts in order to have a $120,000 college fund in 15 years? An APR of 4%, compounded daily

120,000/(1+0.04/365)^(365*15) $65,859.56

4B: (57) Compound Interest. Use CI formula to compute the balance in the accounts. Assume interest is compounded annually (1). 10,000 is invested at an APR of 4% for 10 years.

14,802.44

4A: (21) Find the monthly interest payments in the following situations. Assume that monthly interest rates are 1/12 of annual interest rates. Question: You maintain an average balance of $650 on your credit card, which carries an 18% annual interest rate.

18%/12(annual)=1.5% 1.5%/100=0.015*$650=$9.75

4B: (75) Use the formula for continuous compounding to compute the balance in the following accounts after 1, 5, and 20 Years. Also, find the APY for each account. E^ A $10,000 deposit in an account with an APR of 3.5%

1year- 10,000*e^(0.035x1)=10,356.20 5year- 10,000*e^(0.035x5)=11,912.46 20year- 10,000*e^(0.035x20)=20,137.53 APY: 100(1+0.035/365)^(365)-1 =3.56%

4B: (15) 2^3

2*2*2=8

4C: (24) At age 35, you start saving for retirement. If your investment plan pays an APR of 6% and you want to have $2 million when you retire in 30 years, how much should u have?

2,000,000(0.06/12)/[(1+0.06/12)^12*30-1] =$1991.01

4B: (84) How much must you deposit today into the following accounts in order to have $25,000 in 8 years? An account with daily compounding and an APR of 4%

25,000/(1+0.04/365)^(365*8) $18,154.05

4B: (82) How much must you deposit today into the following accounts in order to have $25,000 in 8 years? An account with quarterly compounding and an APR of 4.5%

25,000/(1+0.045)^(8*4) $17,477.01

4B: (83) How much must you deposit today into the following accounts in order to have $25,000 in 8 years? An account with monthly (8*12) compounding and an APR of 6%

25,000/(1+0.06/12)^(12*8) $15,488.10

4B: (22) 2^3x2^5

2x2x2=8 2x2x2x2x2=32 8x32=256

4A: (20) Compute the total cost per year of the following pairs of expenses. Then complete the sentence: On an annual basis, the first set of expenses is ______% of the second set of expenses. Question: Sandy fills the gas tank of her can an average of once every two weeks at a cost of $35 per tank; her cable TV/Internet service costs $60 per month.

52/2=26(two weeks a year)*$35=$910 $60*12(months in a year)=$720 $910/$720=1.26388....*100=126%

4B: (63) Compounding more than once a year. Use CI formula to compute the balance. 10,000 is invested for 10 years with an APR of 2% and quarterly compounding.

A=$10,000x(1+0.2/4)^(4x10) =$12,207.94

4B: (67) Compounding more than once a year. Use CI formula to compute the balance. $2,000 is invested for 15 years with an APR of 5% and monthly compounding.

A=$2,000*(1+0.05/12)^(12x15) =$4,227.41

4B: (65) Compounding more than once a year. Use CI formula to compute the balance. $25,000 is invested for 5 years with an APR of 3% and daily compounding

A=$25,000*(1+0.03/365)^(365x5) =$29,045.68

4B: Simple Interest problem: P=$100 APR= 10% Y=5 years

A=100*(1+0.1)^5 A=$161.05

4C: (15) Assume monthly deposits and monthly compounding in the following savings plans. Find the savings plan balance after 12 months with an APR of 3% and monthly payments of $150.

A=150[(1+0.03/12)^(12)-1]/(0.03/12) =$1,824.96

4B: Compound Interest problem: P=$224 APR=2% Y=535

A=224*(1+0.02)^535 $8.94 Million

4C: (21) Use the savings plan formula to answer the following questions. You put $300 per month in an investment plan that pays an APR of 3.5%. How much money will you have after 18 years? Compare that to the total deposits made over the time period.

A=300[(1+0.035/12)^(12*18)-1]/(0.035/12) =$90,091.51 12x18x300=64,800

4C: (17) Assume monthly deposits and monthly compounding in the following savings plans.

A=400[(1+0.04/12)^(3*12)-1]/(0.04/12) =$15,272.62

4C: (19) Use the savings plan formula to answer the following questions. At age 25 you set up an IRA with an APR of 5%. at the end of each month, you deposit $75 in the account. How much will the IRA contain when you retire at age 65? Compare that to the total deposits made over the time period.

A=75[(1+0.05/12)^(12*40)-1]/(0.05/12) =$114,451.51 12x40x75=$36,000

4B: Compound Interest Formula for Interest Paid (N) Times Per year: A=P(1+APR/N)^(N*Y)

A=Accumulated balance after Y years P= Starting Principal APR= Annual Percentage Rate N= number of compounding periods per year Y= Number of Years

4C: Savings plan formula:

A=PMT*[(1+apr/n)^(nxy)-1]/(apr/n)

4B: The Compound Interest Formula (for interest paid once a year)

A=Px(1+APR)^1

4B: Quarterly Interest rate: (The Quarterly interest rate is one-fourth of the annual interest rate:)

APR/4

4B: (73) Find the annual percentage yield (to the nearest 0.1%) in the following situations. A bank offers an APR of 1.23% compounded monthly.

APY=100(1+0.0123/12)^(12)-1 1.24%

4B: (71) Find the annual percentage yield (to the nearest 0.1%) in the following situations. A bank offers an APR of 3.1% compounded daily.

APY=100(1+0.031/365)^(365)-1 APY=3.15%

4B: annual percentage yield or APY Formula:

APY=100(1+R/N)^(N)-1

4B: With _______, you receive more than ________, because the interest each year is calculated on your growing balance.

Compound interest; Simple Interest

4B: Interest Paid More than once a year. Interest quarterly, or _____times a year.

Four

cash

Money in the form of bills or coins

4D: Loan Payment Formula:

PMT=p*(APR/n)/[(1-(1+APR/n)^(-ny)] PMT-Regular payment amount P-starting loan principle (amount borrowed) APR-annual percentage rate n-number of payment periods per year y-loan term in years

4B: If $224 is the initial deposit, we refer to this as the _______.

Starting Principle; P

A= P= APR= Y= N=

accumulated balance after Y years starting principle annual percentage rate as a decimal number of years number of compounding periods per year

4C: Annual Return Formula: Your annual return is the average annual rate at which your money grew over the time period.

annual return = (a/p)^(1/y)-1

4C: Yield of A bond formula:

current yield = annual interest payment/current price of bond

4B: (31) 3p=12

p=4

4B: (19) 16^1/2

sqrt(16)=4

4D: % that goes towards principle formula:

starting principle/total loan payment*100%

4B: (41) t/4+5=25

t=80

4D: The percent spent on interest formula:

total loan payment-starting principle/total loan payment

4C: Total Return Formula: Your total return is the percentage change in the investment value over the (Y) period.

total return= new value(A) - starting principle(P)/starting principle(P)*100%

4B: (35) 3x-4=2x+6

x=10

4B: (27) x-3=9

x=12

4D: Finding the total loan payment:

xPayments per year(monthly, quarterly, ect ect)xloan term(typically in years)

4B: Daily Compounding Formula: A=P*(1+APR/365)^(365x1) P=$1000 APR=8% N=365 Y=1

$1000*(1+0.08/365)^(365x1) $1083.28

4A: (13) Compute the total cost per year of the following pairs of expenses. Then complete the sentence: On an annual basis, the first set of expenses is ______% of the second set of expenses. Question: Maria spends $20 every week on coffee and spends $130 per month on food.

$20*(52 weeks in the year)=$1040 $130*(12 Months in a year)=$1560 $1040/$1560=0.6666666666666667*100=67%

4A: (23) Find the monthly interest payments in the following situations. Assume that monthly interest rates are 1/12 of annual interest rates. Question: Vic bought a new plasma TV for $2200. He made a down payment of $300 and then financed the balance though the store. Unfortunately, he was unable to make the first monthly payments and now pays 3% interest per month on the balance.

$2200-$300=$1900 He spends 3% of $1900 Or: 0.03*$1900=$57

4A: (30) Prorate the following expenses and find the corresponding (Monthly) expenses. Question: Randy spends an average of $25 per week on gasoline and $45 every three months on the daily newspaper.

$25*52(weeks in a year)=$1300 12/3(three months in a year)=4*$45=$180 $1300+$180=$1480/12=$123.3

4B: Monthly Compounding Formula: A=P*(1+APR/12)^(12xY) P=$5000 APR=3% N=12(Monthly) Y=5

$5000*(1+0.03/12)^(12x5) $5808.08

4A: (25) Prorate the following expenses and find the corresponding (Monthly) expenses. Question: During one year, Louisa pays $5600 for tuition and fees, plus $400 for textbooks, for each of two semesters.

$5600+$400=$6000 $6000*2=$12000/12=$1000

Bond

A financial security that represents a promise to repay a fixed amount of funds

stock

A share of ownership in a corporation.

4B: Continuous Compounding formula:

A=P*e^(APRxY)

4B: The interest rate is called the _______, or ___.

Annual percentage rate; APR

4B: (81) How much must you deposit today into the following accounts in order to have $25,000 in 8 years? An account with ANNUAL compounding and an APR of 5% (annual is once a year).

P=25,000/(1+0.05)^(8) =$16,920.98

4B: (46) p^(1/3)=3

P=27 (Cuberoot)(3)=27

4B: Compound Interest Formula:

P=A/(1+APR/n)^n*t

4C: Second savings plan formula: (Used for problems that are typically asking for a balance needed to collect interest from such as retirement funds.)

PMT=A*(APR/N)/[(1+APR/N)^(NxY)-1]

4B: With ________ every year you receive the same interest payment.

Simple Interest

4B: annual percentage yield or APY:

The relative increase over one year is called APY. It depends only on the annual interest rate (APR) and the number of compounding periods, not on the starting principle.