MATHEMATICS OF FINANCE Adopted from

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MATHEMATICS OF FINANCEAdopted from
Introductory Mathematical Analysis for Student
of Business and Economics, (Ernest F. Haeussler,
Jr. Richard S. Paul)

• Associated Professor Dr. Dogan N. Leblebici

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MATHEMATICS OF FINANCECOMPOUND INTEREST
WE SHALL USE MATHEMATICS TO MODEL SELECTED TOPICS
IN FINANCE THAT DEAL WITH THE TIME-VALUE OF
MONEY, SUCH AS INVESTMENTS, LOANS, ETC.
PRACTICALLY EVERYONE IS FAMILIAR WITH COMPOUND
INTEREST, WHEREBY THE INTEREST EARNED BY AN
INVESTED SUM OF MONEY (OR PRINCIPAL-capital sum)
IS REINVESTED SO THAT IT TOO EARNS INTEREST. THAT
IS, THE INTEREST IS CONVERTED (OR COMPOUNDED)
INTO PRINCIPAL AND HENCE THERE IS "INTEREST ON
INTEREST."
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCECOMPOUND INTEREST
FOR EXAMPLE, SUPPOSE A PRINCIPAL OF YTL 100 IS
INVESTED FOR TWO YEARS AT THE RATE OF 5 PERCENT
COMPOUNDED ANNUALLY. AFTER ONE YEAR THE SUM OF
THE PRINCIPAL AND INTEREST IS 100 .05(100)
YTL 105. THIS IS THE AMOUNT ON WHICH INTEREST
IS EARNED FOR THE SECOND YEAR, AND AT THE END OF
THAT YEAR THE VALUE OF THE INVESTMENT IS 105
.05(105) YTL 110.25. THE YTL 110.25
REPRESENTS THE ORIGINAL PRINCIPAL PLUS ALL
ACCRUED INTEREST IT IS CALLED THE ACCUMULATED
AMOUNT OR COMPOUND AMOUNT.
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCECOMPOUND INTEREST
THE DIFFERENCE BETWEEN THE COMPOUND AMOUNT AND
THE ORIGINAL PRINCIPAL IS CALLED THE COMPOUND
INTEREST. IN THE ABOVE CASE THE COMPOUND INTEREST
IS 110.25 - 100 YTL 10.25.
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MATHEMATICS OF FINANCECOMPOUND INTEREST
MORE GENERALLY, IF A PRINCIPAL OF P YTL IS
INVESTED AT A RATE OF 100r PERCENT COMPOUNDED
ANNUALLY (FOR EXAMPLE, AT 5 PERCENT, r IS .05),
THEN THE COMPOUND AMOUNT AFTER ONE YEAR IS P Pr
OR P(1 r). AT THE END OF THE SECOND YEAR THE
COMPOUND AMOUNT IS P(1 r) P(1 r)r P(1
r)1 r FACTORING P(1 r)2
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MATHEMATICS OF FINANCECOMPOUND INTEREST
SIMILARLY, AFTER THREE YEARS THE COMPOUND AMOUNT
IS P(1 r)3. IN GENERAL, THE COMPOUND AMOUNT S
OF A PRINCIPAL P AT THE END OF n YEARS AT THE
RATE OF r COMPOUNDED ANNUALLY IS GIVEN BY S
P(1 r)n
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MATHEMATICS OF FINANCECOMPOUND INTEREST

• EXAMPLE 1
• IF YTL 1000 IS INVESTED AT 6 PERCENT COMPOUNDED
  ANNUALLY,
• FIND THE COMPOUND AMOUNT AFTER TEN YEARS.
• FIND THE COMPOUND INTEREST AFTER TEN YEARS.

Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 1 FIND THE COMPOUND AMOUNT AFTER TEN
YEARS. WE USE EQ. (S P(1 r)n ) WITH P
1000, r .06, AND n 10. S 1000(1
.06)10 1000(1.06)10. WE FIND THAT (1.06)10 AS
1.790848. THUS, S 1000(1.790848) YTL 1790.85.
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 1 FIND THE COMPOUND INTEREST AFTER TEN
YEARS. USING THE RESULT FROM PART (A), WE
HAVE COMPOUND INTEREST S P 1790.85 - 1000
YTL 790.85.
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 2 SUPPOSE THE PRINCIPAL OF YTL 1000 IN
EXAMPLE 1 IS INVESTED FOR TEN YEARS AS BEFORE,
BUT THIS TIME THE COMPOUNDING TAKES PLACE EVERY
THREE MONTHS (THAT IS, QUARTERLY) AT THE RATE OF
1.5 PERCENT PER QUARTER. THEN THERE ARE FOUR
INTEREST PERIODS OR CONVERSION PERIODS PER YEAR,
AND IN TEN YEARS THERE ARE 10(4) 40 CONVERSION
PERIODS. THUS THE COMPOUND AMOUNT WITH R .015
IS 1000(1.015)40 1000(1.814018) YTL
1814.02.
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 3 THE SUM OF YTL 3000 IS PLACED IN A
SAVINGS ACCOUNT. IF MONEY IS WORTH 6 PERCENT
COMPOUNDED SEMIANNUALLY, WHAT IS THE BALANCE IN
THE ACCOUNT AFTER SEVEN YEARS? (ASSUME NO OTHER
DEPOSITS AND NO WITHDRAWALS.)
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 3 HERE P 3000, THE NUMBER OF
CONVERSION PERIODS IN 7(2) 14, AND THE RATE PER
CONVERSION PERIOD IS .06/2 .03. BY EQ. (S P(1
r)n ) WE HAVE S 3000(1.03)14
3000(1.512590) YTL 4537.77
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 4 HOW LONG WILL IT TAKE FOR YTL 600 TO
AMOUNT TO YTL 900 AT AN ANNUAL RATE OF 8
PERCENT COMPOUNDED QUARTERLY?
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 4 THE RATE PER CONVERSION PERIOD IS
.08/4 .02. LET N BE THE NUMBER OF CONVERSION
PERIODS IT TAKES FOR A PRINCIPAL OF P 600 TO
AMOUNT TO S 900. THEN FROM EQ. (S P(1 r)n
), 900 600(1.02)n, (1.02)n 900/600 (1.02)n
1.5. TAKING THE NATURAL LOGARITHMS OF BOTH
SIDES, WE HAVE n ln (1.02) ln 1.5, (Prop.
logbmnnlogbm) THE NUMBER OF YEARS THAT
CORRESPONDS TO 20.478 QUARTERLY CONVERSION
PERIODS IS 20.478/4 5.1195, WHICH IS SLIGHTLY
MORE THAN 5 YEARS AND 1 MONTH.
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCECOMPOUND INTEREST
IF YTL 1 IS INVESTED AT A NOMINAL RATE OF 8
PERCENT COMPOUNDED QUARTERLY FOR ONE YEAR, THEN
THE YTL WILL EARN MORE THAN 8 PERCENT THAT YEAR.
THE COMPOUND INTEREST IS S - P 1(1.02)4 l
1.082432 - 1 YTL .082432, WHICH IS ABOUT
8.24 PERCENT OF THE ORIGINAL YTL. THAT IS, 8.24
PERCENT IS THE RATE OF INTEREST COMPOUNDED
ANNUALLY THAT IS ACTUALLY OBTAINED, AND IT IS
CALLED THE EFFECTIVE RATE.
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCECOMPOUND INTEREST
FOLLOWING THIS PROCEDURE, WE CAN SHOW THAT THE
EFFECTIVE RATE WHICH CORRESPONDS TO A NOMINAL
RATE OF r COMPOUNDED N TIMES A YEAR IS GIVEN
BY WE POINT OUT THAT EFFECTIVE RATES ARE
USED TO COMPARE DIFFERENT INTEREST RATES, THAT
IS, WHICH IS "BEST."
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 5 WHAT EFFECTIVE RATE CORRESPONDS TO A
NOMINAL RATE OF 6 PERCENT COMPOUNDED
SEMIANNUALLY?
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCECOMPOUND INTEREST
THE EFFECTIVE RATE IS THE EFFECTIVE RATE IS
6.09 PERCENT.
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 6 TO WHAT AMOUNT WILL YTL 12,000
ACCUMULATE IN 15 YEARS IF INVESTED AT AN
EFFECTIVE RATE OF 5 PERCENT?
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 6 SINCE AN EFFECTIVE RATE IS THE ACTUAL
RATE COMPOUNDED ANNUALLY, WE HAVE S
12,000(1.05)15 12,000(2.078928) YTL 24,947.14.
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 7 HOW MANY YEARS WILL IT TAKE FOR A
PRINCIPAL OF P TO DOUBLE AT THE EFFECTIVE RATE OF
r ?
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 7 LET N BE THE NUMBER OF YEARS IT TAKES.
WHEN P DOUBLES, THEN THE COMPOUND AMOUNT S IS 2P.
THUS 2P P(1 R)N AND SO 2 (1 r)n, ln 2 n
ln (1 r). HENCE, FOR EXAMPLE, IF R .06,
THEN THE NUMBER OF YEARS IT TAKES TO DOUBLE A
PRINCIPAL IS APPROXIMATELY
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 8 SUPPOSE THAT YTL 500 AMOUNTED TO YTL
588.38 IN A SAVINGS ACCOUNT AFTER THREE YEARS. IF
INTEREST WAS COMPOUNDED SEMIANNUALLY, FIND THE
NOMINAL RATE OF INTEREST, COMPOUNDED
SEMIANNUALLY, THAT WAS EARNED BY THE MONEY.
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MATHEMATICS OF FINANCECOMPOUND INTEREST
EXAMPLE 8 LET r BE THE SEMIANNUAL RATE. THERE
ARE SIX CONVERSION PERIODS. THUS, 500(1 r)6
588.38, (1 r)6 588.38/500 THUS THE
SEMIANNUAL RATE WAS 2.75 PERCENT, AND SO THE
NOMINAL RATE WAS 5.5 PERCENT COMPOUNDED
SEMIANNUALLY.
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEPRESENT VALUE
SUPPOSE THAT YTL 100 IS INVESTED FOR ONE YEAR AT
A RATE OF 6 PERCENT COMPOUNDED ANNUALLY. THEN THE
COMPOUND AMOUNT (OR FUTURE VALUE) OF THE YTL 100
IS YTL 106. EQUIVALENTLY, THE VALUE TODAY (OR
PRESENT VALUE) OF THE YTL 106 DUE IN ONE YEAR IS
100. WE CAN GENERALIZE THIS CONCEPT. IF WE SOLVE
THE EQUATION THAT GIVES COMPOUND AMOUNT, NAMELY S
P(1 r)n, FOR P, WE GET P S/(1 r)n. PS
(1r)-n
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEPRESENT VALUE
EXAMPLE A TRUST FUND FOR A CHILD'S EDUCATION IS
BEING SET UP BY A SINGLE PAYMENT SO THAT AT THE
END OF 15 YEARS THERE WILL BE YTL 24,000. IF THE
FUND EARNS INTEREST AT THE RATE OF 7 PERCENT
COMPOUNDED SEMIANNUALLY, HOW MUCH MONEY SHOULD BE
PAID INTO THE FUND INITIALLY?
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEPRESENT VALUE
WE WANT THE PRESENT VALUE OF YTL 24,000 DUE IN
15 YEARS. FROM EQ. (PS (1r)-n) WITH S 24,000,
r .07/2 .035, AND n 15(2) 30, WE HAVE P
24,000(1.035) -30 24,000(.356278) 8550.67.
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MATHEMATICS OF FINANCEPRESENT VALUE
EXAMPLE SUPPOSE MR. SMITH OWES MR. JONES TWO
SUMS OF MONEY YTL 1000 DUE IN TWO YEARS AND YTL
600 DUE IN FIVE YEARS. IF MR. SMITH WISHES TO
PAY OFF THE TOTAL DEBT NOW BY A SINGLE PAYMENT,
HOW MUCH WOULD THE PAYMENT BE? ASSUME AN INTEREST
RATE OF 8 PERCENT COMPOUNDED QUARTERLY.
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MATHEMATICS OF FINANCEPRESENT VALUE
THE SINGLE PAYMENT X DUE NOW MUST BE SUCH THAT
IT WOULD GROW AND EVENTUALLY PAY OFF THE DEBTS
WHEN THEY ARE DUE. THAT IS, IT MUST EQUAL THE SUM
OF THE PRESENT VALUES OF THE FUTURE PAYMENTS. WE
HAVE X 1000(1.02)-8 600(1.02)-20 X1000(.853
490) 600(.672971) 853.490 403.78260
1257.27. THUS, THE SINGLE PAYMENT DUE NOW IS YTL
1257.27.
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MATHEMATICS OF FINANCEPRESENT VALUE
EXAMPLE SUPPOSE THAT YOU HAD THE OPPORTUNITY OF
INVESTING YTL 4000 IN A BUSINESS SUCH THAT THE
VALUE OF THE INVESTMENT AFTER FIVE YEARS WOULD BE
YTL 5300. ON THE OTHER HAND, YOU COULD INSTEAD
PUT THE YTL 4000 IN A SAVINGS ACCOUNT THAT PAYS 6
PERCENT COMPOUNDED SEMIANNUALLY. WHICH INVESTMENT
IS THE BETTER ?
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEPRESENT VALUE
LET US CONSIDER THE VALUE OF EACH INVESTMENT AT
THE END OF FIVE YEARS. AT THAT TIME THE BUSINESS
INVESTMENT WOULD HAVE A VALUE OF YTL 5300, WHILE
THE SAVINGS ACCOUNT WOULD HAVE A VALUE OF
4000(1.03)10 YTL 5375.66. CLEARLY THE BETTER
CHOICE IS PUTTING THE MONEY IN THE SAVINGS
ACCOUNT.
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MATHEMATICS OF FINANCEPRESENT VALUE
EXAMPLE SUPPOSE THAT YOU CAN INVEST YTL 20,000
IN A BUSINESS THAT GUARANTEES YOU THE FOLLOWING
CASH FLOWS AT THE END OF THE INDICATED
YEARS YEAR CASH FLOW 2 YTL 10,000 3 YTL
8,0005 YTL 6,000 ASSUME AN INTEREST RATE OF 7
PERCENT COMPOUNDED ANNUALLY AND FIND THE NET
PRESENT VALUE OF THE CASH FLOWS.
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MATHEMATICS OF FINANCEPRESENT VALUE
SUBTRACTING THE INITIAL INVESTMENT FROM THE SUM
OF THE PRESENT VALUES OF THE CASH FLOWS
GIVES NPV 10,000(1.07)-2 8000(1.07)-3
6000(1.07)-5 - 20,000 10,000(.873439)
8000(.816298) 6000(.712986) - 20,000 8734.39
6530.384 4277.916 - 20,000 -YTL
457.31. NOTE THAT SINCE NPV lt 0, THE BUSINESS
VENTURE IS NOT PROFITABLE IF ONE CONSIDERS THE
TIME-VALUE OF MONEY. IT WOULD BE BETTER TO INVEST
THE YTL 20,000 IN A BANK PAYING 7 PERCENT, SINCE
THE BUSINESS VENTURE IS EQUIVALENT TO ONLY
INVESTING 20,000 - 457.31 YTL 19,542.69.
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MATHEMATICS OF FINANCEANNUITIES
THE SEQUENCE OF NUMBERS 3, 6, 12, 24, 48 IS
CALLED A (FINITE) GEOMETRIC SEQUENCE. THIS IS A
SEQUENCE OF NUMBERS, CALLED TERMS, SUCH THAT EACH
TERM AFTER THE FIRST CAN BE OBTAINED BY
MULTIPLYING THE PRECEDING TERM BY THE SAME
CONSTANT. IN OUR CASE THE CONSTANT IS 2. IF THE
FIRST TERM OF A GEOMETRIC SEQUENCE IS a AND THE
CONSTANT IS r, THEN A SEQUENCE OF TERMS HAS THE
FORM a, ar, ar2, ar3, . . . , arn-1 NOTE THAT
THE RATIO OF EVERY TWO CONSECUTIVE TERMS IS THE
CONSTANT r THAT IS, ar/ar, ar2/ar r,
ETC. (a ? 0). FOR THIS REASON WE CALL r THE
COMMON RATIO. NOTE ALSO THAT THE nTH TERM IN THE
SEQUENCE IS arn-1.
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MATHEMATICS OF FINANCEANNUITIES
THE SEQUENCE OF N NUMBERS a, ar, ar2, . . . ,
arn-1, WHERE a ? 0, IS CALLED A
GEOMETRIC SEQUENCE WITH FIRST TERM a AND COMMON
RATIO r.
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MATHEMATICS OF FINANCEANNUITIES
THE SUM OF GEOMETRIC SERIES
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MATHEMATICS OF FINANCEANNUITIES
THE NOTION OF A GEOMETRIC SERIES IS THE BASIS OF
THE MATHEMATICAL MODEL OF AN ANNUITY. BASICALLY,
AN ANNUITY IS A SEQUENCE OF PAYMENTS MADE AT
FIXED PERIODS OF TIME OVER A GIVEN TIME INTERVAL.
THE FIXED PERIOD IS CALLED THE PAYMENT PERIOD,
AND THE GIVEN TIME INTERVAL IS THE TERM OF THE
ANNUITY. AN EXAMPLE OF AN ANNUITY IS THE
DEPOSITING OF YTL 100 IN A SAVINGS ACCOUNT EVERY
THREE MONTHS FOR A YEAR.
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MATHEMATICS OF FINANCEANNUITIES
THE PRESENT VALUE OF AN ANNUITY IS THE SUM OF THE
PRESENT VALUES OF ALL THE PAYMENTS. IT REPRESENTS
THE AMOUNT THAT MUST BE INVESTED NOW TO PURCHASE
THE PAYMENTS DUE IN THE FUTURE. UNLESS OTHERWISE
SPECIFIED, WE SHALL ASSUME THAT EACH PAYMENT IS
MADE AT THE END OF A PAYMENT PERIOD THAT IS
CALLED AN ORDINARY ANNUITY. WE SHALL ALSO ASSUME
THAT INTEREST IS COMPUTED AT THE END OF EACH
PAYMENT PERIOD.
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MATHEMATICS OF FINANCEANNUITIES
LET US CONSIDER AN ANNUITY OF n PAYMENTS OF R
(YTL) EACH, WHERE THE INTEREST RATE PER. PERIOD
IS r AND THE FIRST PAYMENT IS DUE ONE PERIOD
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MATHEMATICS OF FINANCEANNUITIES
FROM NOW. THE PRESENT VALUE A OF THE ANNUITY IS
GIVEN BY A R(1 r)-1 R(1 r)-2 ... R(1
r)-n. THIS IS A GEOMETRIC SERIES OF n TERMS
WITH FIRST TERM R(1 r)-1 AND COMMON RATIO (1
r)-1. HENCE WE HAVE
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MATHEMATICS OF FINANCEANNUITIES
THUS GIVES THE PRESENT VALUE A OF AN ANNUITY
OF R (YTL) PER PAYMENT PERIOD FOR n PERIODS AT
THE RATE OF r PER PERIOD. THE EXPRESSION 1 (1
r)-n/r IS DENOTED an r AND (LETTING R
1) REPRESENTS THE PRESENT VALUE OF AN ANNUITY
OF YTL 1 PER PERIOD. THE SYMBOL an r IS READ
a ANGLE n AT r. THUS, ARan r
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEANNUITIES
EXAMPLE GIVEN AN INTEREST RATE OF 5 PERCENT
COMPOUNDED ANNUALLY, FIND THE PRESENT VALUE OF
THE FOLLOWING ANNUITY YTL 2000 DUE AT THE END OF
EACH YEAR FOR THREE YEARS, AND YTL 5000 DUE
THEREAFTER AT THE END OF EACH YEAR FOR FOUR YEARS
.
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MATHEMATICS OF FINANCEANNUITIES
EXAMPLE 2000(1.05)-12000(1.05)-22000(1.05)-350
00(1.05)-45000(1.05)-55000(1.05)-6 5000(1.05)-7
YTL 20,762.12
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MATHEMATICS OF FINANCEAMORTIZATION OF LOANS
SUPPOSE A BANK LOANS YOU YTL 1500. THIS AMOUNT
PLUS INTEREST IS TO BE REPAID BY EQUAL PAYMENTS
OF R YTLs AT THE END OF EACH MONTH FOR THREE
MONTHS. FURTHERMORE, LET US ASSUME THAT THE BANK
CHARGES INTEREST AT THE NOMINAL RATE OF 12
PERCENT COMPOUNDED MONTHLY. ESSENTIALLY, FOR YTL
1500 THE BANK IS PURCHASING AN ANNUITY OF THREE
PAYMENTS OF R EACH. USING FORMULA OF THE LAST
SECTION (ANNUITIES),
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEAMORTIZATION OF LOANS
THE BANK CAN CONSIDER EACH PAYMENT AS CONSISTING
OF TWO PARTS (1) INTEREST ON THE OUTSTANDING
(GERI ÖDENMEMIS) LOAN, AND (2) REPAYMENT OF PART
OF THE LOAN. THIS IS CALLED AMORTIZING. A LOAN IS
AMORTIZED WHEN PART OF EACH PAYMENT IS USED TO
PAY INTEREST AND THE REMAINING PART IS USED TO
REDUCE THE OUTSTANDING PRINCIPAL. SINCE EACH
PAYMENT REDUCES THE OUTSTANDING PRINCIPAL, THE
INTEREST PORTION OF A PAYMENT DECREASES AS TIME
GOES ON. LET US ANALYZE THE LOAN DESCRIBED IN THE
EXAMPLE.
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEAMORTIZATION OF LOANS
AT THE END OF THE FIRST MONTH, YOU PAY YTL
510.03. THE INTEREST ON THE OUTSTANDING PRINCIPAL
IS .01(1500) YTL 15. THE BALANCE OF THE
PAYMENT, 510.03 -15 YTL 495.03, IS THEN APPLIED
TO REDUCE THE PRINCIPAL. HENCE THE PRINCIPAL
OUTSTANDING IS NOW 1500 - 495.03 YTL 1004.97.
AT THE END OF THE SECOND MONTH, THE INTEREST IS
.01(1004.97) YTL 10.05. THUS THE AMOUNT OF THE
LOAN REPAID IS 510.03 - 10.05 YTL 499.98, AND
THE OUTSTANDING BALANCE IS 1004.97 - 499.98 YTL
504.99.
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEAMORTIZATION OF LOANS
THE INTEREST DUE AT THE END OF THE THIRD AND
FINAL MONTH IS .01(504.99) YTL 5.05, AND SO THE
AMOUNT OF THE LOAN REPAID IS 510.03 - 5.05 YTL
504.98. HENCE THE OUTSTANDING BALANCE IS 504.99 -
504.98 YTL 0.01. ACTUALLY, THE DEBT SHOULD NOW
BE PAID OFF, AND THE BALANCE OF YTL 0.01 IS DUE
TO ROUNDING. OFTEN, BANKS WILL CHANGE THE AMOUNT
OF THE LAST PAYMENT TO OFFSET THIS. IN THE ABOVE
CASE THE FINAL PAYMENT WOULD BE YTL 510.04. AN
ANALYSIS OF HOW EACH PAYMENT IN THE LOAN IS
HANDLED CAN BE GIVEN IN A TABLE CALLED AN
AMORTIZATION SCHEDULE.
Associated Professor Dr. Dogan N. Leblebici
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MATHEMATICS OF FINANCEAMORTIZATION OF LOANS
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MATHEMATICS OF FINANCEAMORTIZATION OF LOANS
THE TOTAL INTEREST PAID IS YTL 30.10, WHICH IS
OFTEN CALLED THE FINANCE CHARGE. AS MENTIONED
BEFORE, THE TOTAL OF THE ENTRIES IN THE LAST
COLUMN WOULD EQUAL THE ORIGINAL PRINCIPAL WERE IT
NOT FOR ROUNDING ERRORS.
Associated Professor Dr. Dogan N. Leblebici