Interest Factors.pptx

1. 1
Interest Formulas for Compounding

2. 2
CONTENTS
• Single payment series compound amount
• Single payment series present worth
• Practice Problems

3. Types of Compound Interest Formulas
1. Single payment compound amount:
• Here the objective is to find the single future sum (F) of
initial payment P after n period at interest rate i %
compounded every period.
3

4. 4
Q1. A person deposits a sum of Rs.50000 at an interest rate of 15 % compounded
annually for a period of 10 years. Find maturity value after 10 years.

5. 5
Q2. How much money will be accumulated in 25 years if Rs. 800 is deposited one year
from now, Rs. 2400 six years from now, and Rs. 3300, 8 years from now all at an
interest rate of 18 % p.a.?

6. Types of Compound Interest Formulas
2. Single Payment Present Worth Amount:
• Here the objective is to find the present worth amount
(P) of a single future sum (F) which will be received after
n periods at an interest rate of i% compounded at the
end of every interest period.
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7. 7
Q3. A person wishes to have a sum of Rs. 500000 to purchase a car 10 years from now. If
he plans to deposit a lump sum amount which will fetch an interest at the rate of 6%
p.a., Determine the sum.

8. 8
Q4. What is the present worth of Rs.7000 now, Rs. 15000 four years from now and. Rs.
9000 six years from now at an interest rate of 8% p.a.?

9. 9
Practice Problems
1. IDBI came out with an issue of deep discount bonds in the year 2000. The bonds
were offered at a deep discounted rate of Rs. 12750. The maturity period of the
bonds was 30 years with a maturity value of Rs. 500000. Determine the rate of return
on the investment.
Sol: 13 %.
2. A company is planning to make two equal deposits such that 10 years from now
the company will have $49000 to replace a small machine. If the first deposit is made
one year from now and the second nine years from now, how much must be
deposited each time if the interest rate is 15%p.a.
Sol: $10497

10. 10
CONTENTS
• Equal Payment Series (Derivation)
• Equal Payment Series Compound Amount
• Equal Payment Series Sinking Fund
• Practice Problems

11. Types of Compound Interest Formulas
Equal Payment Series- Compound-Amount Factor:
• Suppose we are interested in the future amount F of a fund to which
we contribute A dollars each period and on which we earn interest at a
rate of i per period. The contributions are made at the end of each of
N equal periods
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12. Types of Compound Interest Formulas
• The $A we put into the fund at the end of the first period will be worth
• The $A we put into the fund at the end of the second period will be
worth
• Finally, the last $A that we contribute at the end of the Nth period will
be worth exactly $A at that time.
• This means that there exists a series of the form
Or
12
and so forth…
1

13. Types of Compound Interest Formulas
• Multiplying by (1 + i) results in
• Subtracting 1 from 2
• Solving for F
• The bracketed term is called the equal payment series compound-
amount factor, or the uniform series compound-amount factor; its
factor notation is (F/A, i, N).
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2

14. Types of Compound Interest Formulas
3. Equal Payment Series Compound Amount:
• Here the objective is to find the future worth of n equal
payments which are made at the end of every interest
period till the end of nth interest period at an interest
rate of i % compounded at the end of each interest
period.
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15. 15
Q1. A man deposits $500 in a credit union at the end of each year for 5 years. The
credit union pays 5% interest compounded annually. At the end of 5 years,
immediately after the fifth deposit, how much does the man have in his account?

16. 16
Q2. Formasa Plastics has major fabrication plants in Texas and Hong Kong. The
president wants to know the equivalent future worth of a $1000 capital investment
each year for 8 years, starting 1 year from now. Formasa capital earns at a rate of 14%
per year.

17. Types of Compound Interest Formulas
4. Equal Payment Series Sinking Fund:
• Here the objective is to find the equal amount (A) that
should be deposited at the end of every interest period
for n period to realize a future sum (F) at the end of nth
period at an interest rate of i %.
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18. 18
Q3. How much money must Carol deposit every year starting 1 year from now at 5 ~%
per year in order to accumulate $6000 seven years from now?

19. 19
Q4. Jim Hayes read that out west, a parcel of land could be purchased for $1000 cash.
Jim decided to save a uniform amount at the end of each month so that he would have
the required $1000 at the end of one year. The local credit union pays 0.5% interest.
How much would Jim have to deposit each month?

20. 20
Practice Problems
1. A company deposits $2000 in a bank at the end of every year for 10 years. The
company makes no deposits during the subsequent 5 years. If the bank pays 8%
interest, how much would be in the account at end of 15 years?
Sol: $42560
2. A student wants to have $30000 at graduation 4 years from now to buy a new car.
His grandfather gave him $10000 as a high school graduation present. How much
must the student save each year if he deposits $10000 today and can earn 12% on
both $10000 and his earnings in a mutual fund as his grandfather recommends?
Sol: $2984

21. Types of Compound Interest Formulas
5. Equal Payment Series Present Worth:
•Objective is to the find present worth of an equal payment made at end of every
interest period for n periods.
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22. SolvedProblems
Determine the amount P that you should deposit into an account 2 years
from now, in order to be able to withdraw Rs. 4000/- per year for 5 years
starting 3 years from now, at an interest rate of 15% per year ? Also find
the investment’s current value?
P = ? ; i = 15% ; n=5 ; A= 4000 ;
Notation: P= A(P/A, i, n) = 4000 * (P/A, 15, 5) = 4000 * (3.3522) = Rs
13408.80/-
P1 = P (P/F, 15%, 2) = Rs13408.8 *0.7561 = Rs10138.39
400
0
2
P
i= 15% n=5 years
0 1 3 4 5 6 7 8
400
0
400
0
400
0
400
0
P
1
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23. A company wants to set up a reserve which will help the company to have an annual equivalent amount of Rs
100,000 for next 15 years towards its employee welfare activities. If the welfare activities starts from the beginning
of year 4, and continued till endofyear 15 then find thesinglepayment amountthatneeds to be investedtoday. The
reserveisassumedtogrowatarateof15%.Perannum.
Data Given : A = 100,000; i : 15%, n= 15, P : ?
8
7 9
1
0
1
1
1
2
1
4
1
3
2 3 4 5 6
0 1
1
5
P1
P
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24. • P1 : A ( P/A, i, n) : 100000 (P/A, 15%, 13)
• : 100000*5.5831
• : Rs.558310
• P : P1(P/F, 15%, 2)
• : 558310*0.7561
• P : Rs. 422138.825
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25. Types of Compound Interest Formulas
6. Equal Payment Series Capital Recovery Amount:
•Objective of this mode of investment is to find the annual equivalent
amount (A) which is to be recovered at the end of every interest period
for n interest periods for a loan (P) which is sanctioned now at an interest
rate i% compounded every period.
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26. SolvedProblems
Q1. Rs. 1000/- invested now at 5% interest compounded annually, provide for 8
equal future year end payments. Determine A
Data Given
P = 1000; i = 5% ; n=8 ; A= ?
Notation A= P(A/P, i, n)
= 1000 (A/P , 5 , 8)
= 1000 (0.1547) = Rs. 154.72/-
A= ?
P = 1000
0 1 3 4
2 5
i= 5%
6 7 8
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27. Q2. A bank gives a loan to a company to purchase an equipment worth $10,00,000 at an
interest rate of 18% compoundedannually. Thisamount should be repaid in11 years equal
installments.Findtheinstallmentamountthatcompanyhastopaytothebank?
• P : 10,00,000, i: 18%, n : 11 years. A : ?
A = P ( A/P, I, N)
= 10,00,000 ( A/P, 18%, 11)
= 10,00,000 * 0.2148
= $ 214800 per year
P=10,0000
0
A=?
1 2 3 4 5 6 7 8 9 10 11
0
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28. ARITHMETIC GRADIENT SERIES
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29. Types of Compound Interest Formulas
7. Uniform Gradient Series Annual Equivalent Amount:
•The objective of this mode of investment is to find the annual
equivalent mode of a series with an amount A1 at the end of first
year and with an equal increment (G) at the end of each of the
following n-1 years with the interest rate i % compounded annually.
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30. Solved numerical
1. John and Barbara have just opened two savings accounts at
their credit union. The accounts earn 10% annual interest. John
wants to deposit $1000 in his account at the end of the first year
from now and increase this amount by $300 for each of
the next five years. Barbara wants to deposit an equal annual
deposit so that the two accounts will have equal amount each year
for the next six years. What should be the size of Barbara’s annual
deposit so that the two accounts will have equal balances at the
end of six years?
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31. 31

32. Solved numerical
2. A man is purchasing a small garden tractor. There will be
no maintenance cost during the first 2 years because the
tractor is sold with 2 years free maintenance. For the third
year, the maintenance is estimated at $20. In subsequent
years the maintenance cost will increase by $20 per year
(i.e., fourth-year maintenance will be $40, fifth-year $60,
etc.). How much would need to be set aside now at 8%
interest to pay the maintenance costs on the tractor for the
first 6 years of ownership?
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33. 33

34. Solved numerical
3. Suppose that you make a series of annual
deposits into a bank account that pays 10%
interest. The initial deposit at the end of 1st year
from now is Rs.1,200.The deposit amount
declines by Rs.200 in each of the next 4years.
How much would you have immediately after 5th
deposit?
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35. 35

36. PRACTICE NUMERICALS
• 1. The Macintosh Company has an employee savings plan that
allows every company to invest uoto 5% of his/her annual
salary. The money is invested in company common stock with
the company guaranteeing that the annual return will never be
lass than 8%. Jill was hired at an annual salary of $52,000. She
immediately joined the savings plan investing the full 5% of
her salary each year. If Jill’s salary increases at *% per annum,.
What amount of money is she guaranteed to have at the end of
20years?
• (Ans: F=$224,416)
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37. PRACTICE NUMERICALS
• 2. A-I Box Company is planning to lease a computer system
that will cost (with service) $15,000 in year 1, $16,500 in year
2, and amounts increasing by 10% each year thereafter.
Assume the lease payments must be made at the beginning of
the year and that a 5-year lease is planned. What is the present
worth (year 0) if the interest is16% per year?
• (Ans: P= $67,632)
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