1 4 compound-interest

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  • 1. Compound Interest
  • 2.
    • Compound interest – a type of interest which results from the periodic addition of simple interest to the principal.
    • This type of interest often applies to savings accounts, loans, and credit cards.
    • Compound amount – the amount at the end of the term (after several compounding).
    • It is the sum of the original principal and its compound interest.
  • 3.
    • Formula for the compound amount F :
  • 4.
    • Example. Find the compound amount at the end of 12 periods if the principal is Php25,000 and the interest per period is 10%.
  • 5.
    • Example. What is the maturity value of a 75,000-peso, three-year investment earning 5% compounded monthly?
  • 6.
    • Example. Find the compound amount after 5 years and 9 months if the principal is Php150,500 and the rate is 7% compounded annually.
  • 7.
    • More Formulas:
  • 8.
    • 1. Given P = Php 25,200 , i = 3% , n = 16 , find F .
  • 9.
    • 3. Given P = Php 1.8M , j = 11% , t = 7.5 years, m = 2 , find F .
  • 10.
    • 5. Given F = Php 46,000 , j = 12% , t = 6.25 years, m = 12 , find P .
  • 11.
    • 7. Given F = Php 56,471.27 , P = Php 25,000 , t = 8 years 3 months, m = 4 , find j .
  • 12.
    • 11. Given F = Php 34,500 , P = Php 30,000 , j = 15% , m = 12 , find n .
  • 13.
    • 13. Given F = Php 72,157.25 , P = Php 48,200 , j = 9% , m = 12 , find n .
  • 14.
    • 23. Find the compound amount due in 6 years and 2 months if Php350,000 is invested at 12% compounded monthly.
  • 15.
    • 27. How much must Ella deposit in a bank that pays 11% compounded quarterly so that she will have Php400,000 after 4 years?
  • 16.
    • 28. A personal computer was bought on installments – Php5,000 downpayment and the balance of Php22,000 in 2 years. What is the cash price if the interest rate is 20% compounded quarterly?
  • 17.
    • 30. On April 15, 2011, Justin borrowed Php1.4M. He agreed to pay the principal and the interest at 8% compounded semi-annually on July 15, 2016. How much will he pay then?
  • 18.
    • 33. At what rate converted quarterly will Php30,000 become Php40,000 in 7 years?
  • 19.
    • 37. If Php80,000 is invested at the rate of 6 ½% compounded annually, when will it earn interest of Php15,000?
  • 20.
    • Equation of values – a mathematical statement which says that the dated values of two sets of amounts are equal when brought to a particular point in time (the comparison date).
    • In the context of borrowing, the equation of values says that
    • obligations = payments
    • These sums are obtained by either accumulating or discounting the debts incurred or the payments made toward the comparison date.
  • 21.
    • 45. What single payment at the end of 6 years would replace the following debts?
    • a) Php29,000 due in 1 year without interest
    • b) Php690,000 due in 8 years at 14% compounded quarterly
    • Money is worth 8.5% effective.
    Obligation(s) Payment(s) 1 6 8
  • 22. Obligation(s) Payment(s) 1 6 8
  • 23.
    • 47. For an amount borrowed from a credit cooperative, Janice needs to pay Php100,000 in 5 years. After 2 ½ years , she made a Php50,000 payment. If money is worth 8% compounded semi-annually, how much would she have to pay on the 5th year to fully settle the loan?
    Obligation(s) Payment(s) 2.5 5
  • 24. Obligation(s) Payment(s) 2.5 5
  • 25.
    • 49. If money is worth 8% effective, what single payment in 5 years will repay the following two debts:
    • a) Php125,000 due at once
    • b) Php500,000 due in 8 years
    Obligation(s) Payment(s) 1 5 8
  • 26. Obligation(s) Payment(s) 1 5 8
  • 27.
    • 51. As payments for debts of Php300,000 due at the end of 4 years and Php485,000 at the end of 8 years, Jane agrees to pay Php50,000 at once and Php250,000 at the end of 5 years. She will make a third and final payment at the end of 10 years. How much would it be if money is worth 14% compounded semi-annually.
    Obligation(s) Payment(s) 1 4 5 8 10
  • 28. Obligation(s) Payment(s) 1 4 5 8 10