Math of Finance Semester 1 Unit 2 Page 1 of 19

Name: _________________ Date: ________________

Unit 2.1

Checking Accounts

Use your book or the internet to find the following definitions: Account balance: Deposit: Withdrawal: Direct deposit: ETF: Insufficient funds: Maintenance fee: ATM fees: PROBLEMS:

1. Your checking account balance is $745.05. If you deposit 3 checks for $50, $56.14 and $172.95 and withdraw $100 in cash, what is your new account balance?

2. Your checking account balance is $113.19. If you deposit a check for $50 what is the maximum amount you can withdraw from your checking account without over-drafting your account?

Example

Juliane has a balance of $1350 in her checking account. She deposits a check for $376.12 and withdraws $200. What is her balance after the transactions?

SOLUTION

1350 376.12 200  $1526.12.

3. Create a check register for the transactions listed by filling in the information. The balance in the account is $435.99. a. You write check # 1034 on 1/2/12 for $54.12 to Publix.

b. You withdraw via ATM $50 on 1/4/12.

c. You deposit your paycheck of $432.87 on 1/7/12.

d. You withdraw via ATM $75 on 1/10/12. There is a $2.95 fee associated with the transaction since the ATM is not affiliated with your bank.

e. You pay off your credit card with $372.15 on 1/15/12. f. You write a check for $32.12 to Kroger on 1/31/12

Number Date Description of Transaction Debit (-) Credit (+) Balance

Unit 2.2

Reconciling a Bank Statement

How do you make sure that your records are correct? Reconciling a bank statement with your checking book register is a means to make sure that your records are in line with the bank’s records.

Use your book or the internet to find the following definitions and explain what the terms mean in your own words: Starting balance:

Ending balance:

Outstanding checks:

Example

Below are your check register and your bank statement. Reconcile your check register with your bank statement.

Number Date Description of Transaction Debit (-) Credit (+) Balance

Previous Balance $653.00

103 2/5/12 Publix $26.76 $626.24

104 2/7/12 Kroger $45.29 $580.95

2/15/12 ATM $100.00 $480.95

2/17/12 Deposit pay check $498.12 $979.07

105 2/25/12 BestBuys $103.21 $875.86

DATE DESCRIPTION CHECK NUMBER AMOUNT BALANCE

2/1/12 Starting Balance 653.00 2/5/12 Withdrawal 103 26.76 626.24 2/7/12 Withdrawal 104 45.29 580.95 2/15/12 Withdrawal 100.00 480.95 2/17/12 Deposit l 498.12 979.07 2/29/12 Service Charge 5.00 974.07 2/29/12 Ending Balance 974.07 Solution:

The ending balances of the check register and bank statement do not match. The reason is you wrote a check which is outstanding (#105) and you did not include the bank service fee. In order to match the records you have to subtract the service fee ($5.00) from your check register balance and subtract the outstanding check ($103.21) from your ending balance of your bank statement.

PROBLEMS:

1. Below are your check register and your bank statement. Reconcile both so that they match.

Number Date Description of Transaction Debit (-) Credit (+) Balance

Previous Balance $278.23

123 3/1/12 Publix $67.34 $210.89

124 3/10/12 Superior Apartments $20.91 $189.98

2/15/12 ATM $150.00 $39.98

2/17/12 Deposit pay check $782.12 $822.10

125 2/20/12 WalMart $69.34 $752.76

DATE DESCRIPTION CHECK NUMBER AMOUNT BALANCE

3/1/12 Starting Balance 278.23 3/5/12 Withdrawal 123 67.34 210.89 3/13/12 Withdrawal 124 20.91 189.98 3/15/12 Withdrawal 150.00 39.98 3/17/12 Deposit l 782.12 822.10 3/31/12 Service Charge 10.00 812.10 3/31/12 Ending Balance 812.10

Unit 2.3

Savings Accounts

Use your book or the internet to describe following terms in your own words: Savings account

Interest

Principal

Money market account

Certificate of deposit (CD)

PROBLEMS:

1. Rank the interest rates from lowest to highest: 3 %, 3.73%, 3 %, 33 5 9%, 3 %.1

4 8 16 2

2. You want to deposit $5000 in a certificate of deposit for a period of 2 years. You visit with 4 banks and you are quoted the following rates:

Wells Fargo: 4 %1

2 Bank of America:4.52% First National: 7 4 % 16 Peoples Bank: 5 4 % 8

Which bank has the highest interest rate? Example

You want to deposit $8000 in a certificate of deposit for a period of 2 years. You visit with 4 banks and you are quoted the following rates:

Wells Fargo: 4 %1

4 Bank of America:4.22% First National: 3 4 % 8 Peoples Bank:4.31% SOLUTION Wells Fargo: 4 %1 4 1 4 0.25 4.25% 4    4  Bank of America:4.22% First National:4 %3 4 3 4 0.375 4.375% 8    8  Peoples Bank:4.31%

PROBLEMS:

3. Mark deposits $7500 in an account that pays 3.25% simple interest. He keeps the money in the account for 2 years without any deposits or withdrawals. How much is in the account after 2 years?

4. Cindy deposits $36700 in an account that pays 7½ % simple interest. She keeps the money in the account for 5 years without any deposits or withdrawals. How much is in the account after 5 years?

5. Chris deposits $175000 in an account that pays 6¼ % simple interest. He keeps the money in the account for 10 years without any deposits or withdrawals. How much is in the account after 10 years?

6. John deposits $500 in an account that pays 1.25% simple interest. He keeps the money in the account for 1 years without any deposits or withdrawals. How much is in the account after 1 year?

Example

Mitt deposits $1200 in an account that pays 4.5% simple interest. He keeps the money in the account for 3 years without any deposits or withdrawals. How much is in the account after 3 years?

SOLUTION

Use the simple interest formula, Iprt. (where pprincipal, rinterest rate, ttime in years) 1200 0.045 3 162

I prt   

PROBLEMS:

7. You invest $125000 in a simple interest account for 7 years. What interest rate must the account pay so there is $150000 at the end of 7 years?

8. You invest $800 in a simple interest account for 2 years. What interest rate must the account pay so there is $850 at the end of 2 years?

9. You want to buy a car for $18000. You have saved up $15000. You invest the $15000 in a simple interest account for 3 years. What interest rate must the account pay so there is $18000 at the end of 3 years so that you can buy the car?

Example

You invest $5000 in a simple interest account for 5 years. What interest rate must the account pay so there is $6000 at the end of 5 years?

SOLUTION

Subtract to find the interest, I6000 5000 1000.  The interest is $1000. Use the simple interest formula,I prt:

Solve the simple interest formula in terms of r,which is the interest rate: r I pt



Plug in the values for I p and t, , to solve 1000 0.04 4% 5000 5

r  

Unit 2.4

Compound Interest

Use your book or the internet to describe following terms in your own words: Compound interest

Annual compounding

Semiannual compounding

Quarterly compounding

Daily compounding

PROBLEMS:

1. Maria deposits $3000 in a savings account that pays 4% interest, compounded semiannually. What is her balance after 1 year?

2. Maria deposits $2000 in a savings account that pays 8% interest, compounded semiannually. What is her balance after 3 years?

3. Maria deposits $5000 in a savings account that pays 7% interest, compounded quarterly. What is her balance after 2 years?

Example

Maria deposits $1000 in a savings account that pays 6% interest, compounded semiannually. What is her balance after 1 year?

SOLUTION

Convert 6% to a decimal r6%0.06 Convert 6 months to years t6month0.5years

Use the simple interest formula I prt

Substitute and simplify I 1000 0.06 0.5  30 Add the interest to the principal 1000 30 1030 

This new principal of $1030 is used to compute the next six months’ interest. Use the simple interest formula I prt

Substitute and simplify I 1030 0.06 0.5  30.90 Add the interest to the principal 1030 30.90 1060.90  Maria’s balance is $1060.90 after one year.

Compare that to the balance if you have simple interest for one year. The interest after one year is 1000 0.06 1 60

Unit 2.5

Compound Interest Formula

Use your book or the internet to describe following terms in your own words: Annual percentage rate

Annual percentage yield

The compound interest formula is

1

nt

r

B

p

n







_



_





where Bending balance

p principal or original balance

r



interest rate expressed as decimal

n



number of times interest is compounded annually

t



number of years

Example

You deposit $1650 for three years at 3% interest, compounded daily. A. What is her ending balance?

B. What is the interest accumulated? SOLUTION

Use the compound interest formula. The values for the variables arep1650,r0.03,n365,t3..

Substitute the values into the compound interest formula:

365(3)

0.03

1

1650 1

1805.38

365

nt

r

B

p

n











_



_



_



_











Your ending balance is $1805.38.

PROBLEMS:

1. You deposit $3000 in a savings account that pays 4% interest, compounded daily. What is your balance after 3 years? What is the accumulated interest?

2. You deposit $17000 in a savings account that pays 8% interest, compounded daily. What is your balance after 15 years? What is the accumulated interest?

3. Jack deposits $6500 in a savings account that pays 5.75% interest, compounded daily. What is your balance after 2 years? What is the accumulated interest?

4. Jack deposits $6500 in a one-year CD that pays 5.75% interest, compounded daily. What is the annual percentage yield?

5. You deposit $2500 in a one-year CD that pays 6.5% interest, compounded daily. What is the annual percentage yield?

Example

You deposit $8000 for one year at 3.2% interest, compounded daily. What is the annual percentage yield (APR)? SOLUTION

Use the APY formula

1

1

n

r

APY

n





 

_

_







. The values for the variables arer0.032,n365.. Substitute the values into the APY formula:

365

0.032

1

1 0.0325

3.25%

365

APY

 



_



_

 







Unit 2.6

Continuous Compounding

Use your book or the internet to describe following terms in your own words: Continuous compounding

PROBLEMS:

1. You deposit $3000 in a savings account that pays 4%, compounded continuously. What is your balance after 3 years? What is the accumulated interest?

2. You deposit $5500 in a savings account that pays 2.5%, compounded continuously. What is your balance after 7 years? What is the accumulated interest?

3. You deposit $120000 in a savings account that pays 6.5%, compounded continuously. What is your balance after 40 years? What is the accumulated interest?

Example

You deposit $1000 for at 4.3% interest, compounded continuously. What is your ending balance after five years? SOLUTION

Use the Continuous Compound Interest Formula:









exp

2.72

int

rt

B

pe

where B

ending balance

p

principal

e

onetntial base

r

erest rate decimal

t

number of years















. 0.043 5 1000 $1239.86 B e  

Unit 2.7

Future Value of Investments

Use your book or the internet to describe following terms in your own words: Future value of a single investment

Future value of a periodic deposit investment

PROBLEMS:

1. At the age of 25 you make a single deposit of $30,000 into a mutual fund that invests in Dow Jones stocks. Historically stocks in the Dow Jones returned 10% annually. If you expect the same return for the future what will be the amount of money in the mutual fund by the time you are 60 years old?

Example

You deposit $15000 in a mutual fund. You expect an annual return of 9.5%, compounded continuously. What is your ending balance after 40 years? What is the amount of money you earned on the investment?

SOLUTION









exp

2.72

int

rt

B

pe

where B

ending balance

p

principal

e

onetntial base

r

erest rate decimal

t

number of years















0.095 40 15000 $670,517.77 rt B pe  e  

PROBLEMS:

1. At the age of 25 you start making yearly periodic payments of $3,000 into a mutual fund. You expect yearly returns of 12%, compounded annually. What is the expected account balance when you are 65?

2. You save up for a car which is $25000. You start saving $2000 every year and put it into a savings account whith an annual interest rate of 8.5%, compounded yearly. Will you have enough money if you save for 10 years? Example

You are 30 years old and open a savings account with Bank of America. You plan to invest $5000 each year until you are at the age of 50. The expected interest is 4.5%, compounded annually. What is the expected account balance when you are 50 years old?

SOLUTION

Use the formula of a periodic deposit investment





((1

)

1)

int

int

nt

r

P

n

B

where B

ending balance

r

n

P

periodic deposit amount

r

annual

erest rate decimal

n

number of times

erest is compounded annually

t

length of investment in years

















1(20) 0.045 5000((1 ) 1) 1 _$156,857.11 0.045 1 B    

Unit 2.8

Present Value of Investments

Use your book or the internet to describe following terms in your own words: Present value of a single investment

Present value of a periodic deposit investment

Example

Your parents know that in 6 years you will go to college. They will need $20,000 for the first year’s tuition. How much should your parents deposit into an account that yields 5% interest, compounded annually, in order to have that amount? Round your answer to the nearest thousand dollars.

SOLUTION

Use the formula for the Present Value of a Single Deposit Investment









(1 ) int int nt B

P where B ending balance

r n

p principal or original balance present value r erest rate decimal

n number of times erest is compounded annually t number of years        1(6) 20000 $14,924.31 0.05 (1 ) (1 ) 1 nt B P r n     

PROBLEMS:

1. Bob wants $30,000 at the end of 7 years in order to buy a car. If his bank pays 4.2% interest, compounded annually, how much must he deposit now to reach his goal?

2. Your grandpa wants to open an account for you that he hopes will have $80,000 in it after 20 years. How much must he deposit now into an account that yields 2.75% interest, compounded monthly, so he can reach his goal?

3. Rick needs a $50,000 down payment for a house in 5 years from now. How much must he deposit now into an account that yields 6% interest, compounded quarterly, so he can reach his goal?

PROBLEMS:

1. Bob wants $30,000 at the end of 7 years in order to buy a car. If his bank pays 4.2% interest, compounded annually, how much must he deposit monthly to reach his goal?

2. Your grandpa wants to open an account for you that he hopes will have $80,000 in it after 20 years. How much must he deposit yearly into an account that yields 2.75% interest, compounded annually, so he can reach his goal?

3. Rick needs a $50,000 down payment for a house in 10 years from now. How much must he deposit monthly into an account that yields 6% interest, compounded quarterly, so he can reach his goal?

Example

Your parents know that in 3 years you will go to college. They will need $15,000 for the first year’s tuition. How much should your parents deposit monthly into an account that yields 4% interest, compounded annually, in order to have that amount? Round your answer to the nearest hundred dollars.

SOLUTION

Use the formula for the Present Value of a Periodic Deposit Investment





(1

)

1

int

nt

r

B

n

P

where B

ending balance

r

n

P

Periodic Investment

r

erest rate decimal

n

number of times you make a deposit per year

t

number of years



















12(3) 0.04 15000 12 _$392.86 0.04 (1 ) 1 (1 ) 1 12 nt r B n P r n         