# general math ( finals topics).pdf

7. Nov 2022
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### general math ( finals topics).pdf

• 1. MATHEMATICS OF FINANCE INTEREST: > Is a fraction or percentage being imputed to a sum of money. SIMPLE INTEREST: > Is essentially the interest charged to a borrower or earned by a lender for the full term of the loan.
• 2. • FORMULA: I = P x R x T Where: I = interest P = Principal R = Rate T = time
• 3. • TIME CONVERSION: • > IF THE TIME IS IN TERMS OF: • MONTHS, DIVIDE BY 12. • SEMIANNUALLY, DIVIDE BY 2. • QUARTERLY, DIVIDE BY 4. • SEMIMONTHLY, DIVIDE BY 24. • > IF THE TIME IS EXPRESSED IN DAYS: • EXACT INTEREST: t = number of days/ 365 • ORDINARY INTEREST: t =number of days/ 360
• 4. PRINCIPAL : The sum of money that someone borrows. RATE : is a percentage of the principal amount. TIME: is the agreed date or period when the loan will be paid in full.
• 5. • 1. Given: • P = P10,000 • R= 5 % per month • Time = 5 months • I = ? • 2. Given: • I = P 6,000 • P = P 20,000 • R = 8% per year • T = ? 3. Given: R = 15% per month Time = 6 months I = P 4,500 P = ? 4. Given: P = P 30,000. I = P 9,000. R = ? ( per month) T = 3 months
• 6. MATURITY AMOUNT OR FINAL AMOUNT: ( for simple interest) Is the amount to be paid to the holder of a financial obligation at the obligation’s maturity. FINAL AMOUNT FORMULA: F = P + I or F = P ( 1 + rt) r = F – P/ Pt t = F –P/ Pr
• 7. 1. GIVEN: P = 100,000 R = 8% per annum T = 5 years I = ? F = ? 2. GIVEN: F= P 200,000 P = P 100,000 T = 7 years R = ?
• 8. COMPOUND INTEREST: Is similar to simple interest, only that the interest charged or earned is being rolled – up and reinvested with the principal amount. The sum by which the original principal has increased by the end of the term of the investment.
• 9. The conversion period it can be: • Quarterly ( 4 periods) • Semiannually( 2 periods) • Monthly ( 12 months)
• 10. FORMULA: n F = P( 1 + i) Where: F=Maturity amount P = Principal amount i = Interest rate per conversion( expressed as decimal ) i = j / m j : annual rate , m = number of conversion periods per year n= number of conversion periods
• 11. • Example 1. Accumulate P 5,000 for 3 years at 10% compounded quarterly. Given: P = P5,000 n=3(4) = 12 i = j/m = 10%/ 4 = .10/4 = 0.025
• 12. • Example 2 • Find the amount due at the end of 6 ¾ years if P 2,000 is invested at 12% compounded monthly. • Given: • i=j /m = .12/ 12 = .01 • P = p2,000 • n=12(6 ¾) =81
• 13. • MATURITY AMOUNT in Compound amount • Formula: -n M = F ( 1 + I ) or F = n ( 1 + i) Where: M = Maturity amount
• 14. • 1. Find the maturity amount of p5,000 due in 6 years if money is worth 12% compounded semiannually. • 2. If money can be invested at 12% compounded semiannually, find the maturity amount of p1,000 due at the end of 5 ½ years.