LU7 Mathematics of Finance_Answer.pptx - LU 7 MATHEMATICS OF FINANCE \u2022 Simple Interest \u2022 Compound Interest \u2022 Annuities \u2022 Amortization and

LU7 Mathematics of Finance_Answer.pptx - LU 7 MATHEMATICS...

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LU 7 MATHEMATICS OF FINANCE Simple Interest Compound Interest Annuities Amortization and Sinking Funds 1
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EXAMPLE 2: TRUST FUNDS An amount of $2000 is invested in a 10 -year trust fund that pays 6% annual simple interest . What is the total amount of the trust fund at the end of 10 years ? 2
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EXAMPLE 2 SOLUTION: TRUST FUNDS An amount of $2000 is invested in a 10 -year trust fund that pays 6% annual simple interest .What is the total amount of the trust fund at the end of 10 years ? Solution The total amount is given by or $3200 . 3 (1 ) 2000[1 (0.06)(10)] 3200 A P rt
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EXAMPLE 3 – FUTURE VALUE AND PRESENT VALUE An investor wants to have $20,000 in 9 months. If the best available interest rate is 6.05% per year, how much must be invested now to yield the desired amount? 4
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EXAMPLE 3 – FUTURE VALUE AND PRESENT VALUE An investor wants to have $20,000 in 9 months. If the best available interest rate is 6.05% per year, how much must be invested now to yield the desired amount? S = P + I = P + Prt . 5
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EXAMPLE 5 – PERIODIC COMPOUNDING For each of the following investments, find the interest rate per period, i , and the number of compounding periods, n . (a) 12% compounded monthly for 7 years (b) 7.2% compounded quarterly for 11 quarters 6
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EXAMPLE 5 – PERIODIC COMPOUNDING For each of the following investments, find the interest rate per period, i , and the number of compounding periods, n . (a) 12% compounded monthly for 7 years If the compounding is monthly and r = 12% = 0.12, then i = 0.12/12 = 0.01. The number of compounding periods is n = (7 yr)(12 periods/yr) = 84. (b) 7.2% compounded quarterly for 11 quarters i = 0.072/4 = 0.018, n = 11 (the number of quarters given) 7
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EXAMPLE 6 – ANNUAL COMPOUNDING If $3000 is invested for 4 years at 9% compounded annually, how much interest is earned? Solution: The future value is S = $3000(1 + 0.09) 4 = $3000(1.4115816) = $4234.7448 = $4234.74, to the nearest cent 8 Because $3000 of this amount was the original investment, the interest earned is $4234.74 $3000 = $1234.74 .
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EXAMPLE 7 Find the total amount of RM10,000 after 5 years invested at a rate of 3% and compounded as followed: (a)Annually (b)Quarterly (c)Semiannually (d)Monthly (e)Continuously Which of the investments above is the best? 9
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EXAMPLE 7A SOLUTION P = RM10,000 n = 5 years r = 3% (a)Annually 10 5 ) 1 ( 5 03 . 0 1 03 . 0 nk k r 74 . 592 , 11 03 . 1 000 , 10 1 03 . 0 1 000 , 10 1 5 ) 1 ( 5 RM S k r P S nk 74 . 592 , 11 ) 03 . 1 ( 000 , 10 ) 03 . 0 1 ( 000 , 10 ) 1 ( 5 5 RM S S S r P S n
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EXAMPLE 7B SOLUTION P = RM10,000 n = 5 years r = 3% (b)Quarterly 11 20 ) 4 ( 5 0075 . 0 4 03 . 0 nk k r 84 . 611 , 11 0075 . 1 000 , 10 ) 0075 . 0 1 ( 000 , 10 ) 1 ( 20 20 RM S r P S n
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EXAMPLE 7C SOLUTION P = RM10,000 n = 5 years r = 3% (c)Semiannually 12 10 ) 2 ( 5 015 . 0 2 03 . 0 nk k r 41 . 605 , 11 015 . 1 000 , 10 ) 015 . 0 1 ( 000 , 10 ) 1 ( 10 10 RM S r P S n
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EXAMPLE 7D SOLUTION P = RM10,000 n = 5 years r = 3% (d)Monthly 13 60 ) 12 ( 5 0025 . 0
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