Name________________________________ UDC – Quantitative Reasoning I EXAMINATION 3 – Personal Finance – Exponential Functions Fall - 2012 Instructions: This exam is worth 100 points. Read each question carefully. Answer each question clearly and concisely. Please, show All of Your Work. Remember, I do not believe in magic!!!

A) B) Answer C) D)

1. What is the simple interest for a principal of $620 invested at a rate of 7% for 3 years? $173.60 $130.20 $172.60 $129.20

A) B) C) Answer D) E)

2. If you borrow $1100 for 5 years at 14% annual simple interest, how much must you repay at the end of the 5 years? $770.00 $2215.13 $2117.96 $77,000 $1870.00

A)Answer B) C) D)

3. How much interest is earned in 5 years on $2,900 deposited in an account paying 7.1% interest, compounded quarterly? $1,223.07 $1,186.44 $266.68 $1,029.50

A)Answer B) C) D) E)

4. Suppose Emily Yu deposited $1300 in an account that earned simple interest at an annual rate of 8% and left it there for 4 years. At the end of the 4 years, Emily deposited the entire amount from that account into a new account that earned 8% compounded quarterly. She left the money in this account for 4 years. How much did she have after the 8 years? $2355.70 $2427.96 $3233.87 $2457.65 $4850.81

A) B) C) Answer D)

5. If $1,390 is invested in an account which earns 9% interest compounded annually, which will be the balance of the account at the end of 14 years? $11,106,193 $3141 $4645 $21,211

A) B) C) Answer D)

6. Susan bought a 6-month $1100 certificate of deposit. At the end of 6 months, she received $99 simple interest. Find the annual rate of simple interest paid. 18% 16% 15.0% 9%

A) B) Answer C)

7. What lump sum should be deposited in an account that will earn at an annual rate of 8%, compounded quarterly, to grow to $140,000 for retirement in 15 years? $137,052.73 $42,335.45 $24,137.93

...COMPOUNDINTEREST
Making or Spending Money
SIMPLE INTEREST FORMULA
If a principal of P dollars is borrowed for a
period of t years at a per annum interest rate
r, expressed as a decimal, then interest I
charged is
I Pr t
This interest is not used very often. Interest is
usually compounded which means interest
is charged or given on the interest and the
principal.
Simple Interest Example
COMPOUNDINTEREST
Payment Periods:
Annually
Once per year
Semiannually
Twice per year
Quarterly
Four times per year
Monthly
Twelve times per year
Weekly
Fifty two times per year
Daily
365 (360 by banks) per year
COMPOUNDINTEREST FORMULA
The amount A after t years due to a principal
P invested at an annual interest rate r
compounded n times per year is
r
A P 1
n
nt
A is commonly referred to as the
accumulated value or future value of the
account. P is called the present value.
COMPOUNDINTEREST
Example:
Investing $1000 at an annual rate of 8%
compounded annually, quarterly, monthly,
and daily will yield the following amounts
after 1 year:
Annually
Quarterly
Monthly
Daily
COMPOUNDINTEREST
On-line example
More on-line examples
COMPOUND...

...*CompoundInterest/Discount*
CompoundInterest
When you borrow money from a bank, you pay interest. Interest is really a fee charged for borrowing the money, it is a percentage charged on the principle amount for a period of a year - usually.
If you want to know how much interest you will earn on your investment or if you want to know how much you will pay above the cost of the principal amount on a loan or mortgage, you will need to understand how compoundinterest works.
* Compoundinterest is paid on the original principal and on the accumulated past interest.
.
Conversion periods are:
Semi-Annually = (m = 2)
Annually = m = 1 / P × (1 + r) = (annual compounding)
Quarterly = m = 4 / P (1 + r/4)4 = (quarterly compounding)
Monthly = m = 12 / P (1 + r/12)12 = (monthly compounding)
The fundamental formula for compound amount is:
F = P(1 + i)n
F = compound amount
P = original principal
i = interest per conversion period which is equal to nominal rate (j) divided by the conversion period (m)
n = total number of conversions period for the whole term; (m * t)
Illustrative Examples:
1.) Find the compoundinterest on P1,000 at the end of 8 ½ years at 8% compounded quarterly.
P = P1,000 j =...

...Chapter 5, 6 Review
1. You invested $1,650 in an account that pays 5 percent simple interest. How much more could you have earned over a 20-year period if the interest had compounded annually?
A. $849.22
B. $930.11
C. $982.19
D. $1,021.15
E. $1,077.94
2. Today, you earn a salary of $36,000. What will be your annual salary twelve years from now if you earn annual raises of 3.6 percent?
A. $55,032.54
B. $57,414.06
C. $58,235.24
D. $59,122.08
E. $59,360.45
3. You hope to buy your dream car four years from now. Today, that car costs $82,500. You expect the price to increase by an average of 4.8 percent per year over the next four years. How much will your dream car cost by the time you are ready to buy it?
A. $98,340.00
B. $98,666.67
C. $99,517.41
D. $99,818.02
E. $100,023.16
4. Your father invested a lump sum 26 years ago at 4.25 percent interest. Today, he gave you the proceeds of that investment which totaled $51,480.79. How much did your father originally invest?
A. $15,929.47
B. $16,500.00
C. $17,444.86
D. $17,500.00
E. $17,999.45
5. What is the present value of $150,000 to be received 8 years from today if the discount rate is 11 percent?
A. $65,088.97
B. $71,147.07
C. $74,141.41
D. $79,806.18
E. $83,291.06
6. You would like to give your daughter $75,000 towards her college education 17 years from now. How much money must you set aside today for this purpose if you can earn 8 percent on your...

...savings account. Suppose you have a choice of keeping your money for five years in a savings account with a 2% interest rate, or in a five year certificate of deposit with and interest rate of 4.5%. Calculate how much interest you would earn with each option over five years time with continuous compounding.
I’m going to do this for my checking and savings account amount
Checking Account
A = Ce^RT My total money in the checking account is 2100 dollars Since the formula for the continuous compounding is A=Ce^RT where C is the initial deposit or capital, T for time, R is the rate of interest and A will be the final amount.
Capital = 2100, Interest Rate ( R) = 2% Time (T) = 5 years, e = 2.7182818284
When money kept for five years in a savings account with a 2% interest rate:
By using the values into formula:= 2100 e ^(0.02*5) = 2318.57
Interest earned = 2318.57 – 2100 = 218.57 dollars
Five year certificate of deposit with interest rate of 4.5%.So A = Ce^RT 2100e^4.5*5=2680.19 - 2100=$516.98
Savings Account = P*e^rt = Pe^(0.02*5) = Pe^0.1 = 1.105171P
Therefore, Interest = A - P = 0.105171P
Amount with certificate of deposit account = P*e^rt = Pe^(0.045*5) = Pe^0.225
= 1.252323P
Therefore, Interest = A - P = 0.252323P
A = 10,000e^(.02*5) = $11051.71 <-- 2%
A = 10,000e^(.045*5) = $12,523.23 <--4.5%
(I would opt for...

...Compounded Interest
Mathematics: MATH650 section 02
Wendy Forbes
April 27, 2010
We often hear people say that we should let our money work for us.
Using money or capital for income or profit is called an investment.
An accountant manages a company’s money. Then, managers or company investors review their reports to find out the financial status. The demand for accountants increases as more private companies are established. In addition, there are always new and changing laws that increase the need for a person with these skills.
Continuously Compounded interest is what banks normally use to calculate the interest on investments. This method is the equal of continually recalculating the interest based on the current principal amount.
There are different types of CompoundInterest. Interest is the amount of money earned in a saving account.
* Simple Interest: Interest calculated once on the principal.
* CompoundInterest: Interest calculated for a given segment of time of the investment. For example, compounded monthly, means the interest is calculated each month and combined with the principal. So, for the next month, interest is earned on the interest.
Continuously CompoundInterest Formula...

...Compoundinterest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on. This addition of interest to the principal is called compounding. A bank account, for example, may have its interest compounded every year: in this case, an account with $1000 initial principal and 20% interest per year would have a balance of $1200 at the end of the first year, $1440 at the end of the second year, $1728 at the end of the third year, and so on.
To define an interest rate fully, allowing comparisons with other interest rates, both the interest rate and the compounding frequency must be disclosed. Since most people prefer to think of rates as a yearly percentage, many governments require financial institutions to disclose the equivalent yearly compounded interest rate on deposits or advances. For instance, the yearly rate for a loan with 1% interest per month is approximately 12.68% per annum (1.0112 − 1). This equivalent yearly rate may be referred to as annual percentage rate (APR), annual equivalent rate (AER), effective interest rate, effective annual rate, and other terms. When a fee is charged up front to obtain a loan, APR usually counts that cost as well as the compoundinterest in converting to...

...number of shares owned by the CEO.
b) The Fine Company’s total profit for the year was $300 000. Determine the P/E ratio (price to earnings ratio) for Fine Company, assuming that the CEO and CFO together own 5% of the number of stocks in the company. (Remember that price=price per share and earnings= profit earned per share)
3. The ratio of males:females in the 1st year at TRSM is 5:4 this year. If the school had admitted 200 more males, the ratio would have been 3:2. Find the number of students actually admitted this year.
4. a) Solve the system of equations:
b) If you graph both of these lines, what does the answer you found represent?
c) Graph both lines and verify your answer graphically.
5. The following equations represent lines that are a) parallel b) intersecting c) are the same line. Circle the correct answer.
3x-6y = 7
9x-18y=20
6. It turns out that $1 CAN is worth 0. 63 euros. When I go to Europe and get ready to return to Canada, I have 500 Euros left, which I exchange. The person cannot give me change and always rounds down to the nearest Canadian dollar, in order to make a profit. How many Canadian dollars do I get back? How much profit does she make?
7. Solve for x:
8. The following chart represents a survey done on cellphone use as shown.
| Cellphone | No Cellphone | Total |
Under 25 | 600 | 100 | |
25 or over | 260 | 320 | |...

...13.1 CompoundInterest
• Simple interest – interest is paid only on the
principal
• Compoundinterest – interest is paid on both
principal and interest, compounded at regular
intervals
• Example: a $1000 principal paying 10% simple
interest after 3 years pays .1 3 $1000 = $300
If interest is compounded annually, it pays .1
$1000 = $100 the first year, .1 $1100 = $110
the second year and .1 $1210 = $121 the third
year totaling $100 + $110 + $121 = $331 interest
13.1 CompoundInterest
Period
Interest
Credited
Times
Credited
per year
Rate per
compounding
period
Annual
Semiannual
year
1
6 months 2
Quarterly
quarter
4
R
4
Monthly
month
12
R
12
R
R
2
13.1 CompoundInterest
• Compoundinterest formula:
M P (1 i )
n
and
I M P
M = the compound amount or future value
P = principal
i = interest rate per period of compounding
n = number of periods
I = interest earned
13.1 CompoundInterest
• Time Value of Money – with interest of 5%
compounded annually.
2000
$1000 $1000
n
(1 i )
(1.05)10
2010
$1000
2020
$1000(1 i ) n
$1000(1.05)10
13.1 CompoundInterest
• Example: $800 is...

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