Chapter 2 : Profit, Loss, Simple Interest and Compound Interest

Topics covered in this snack-sized chapter:



Cost Price arrow_upward


  • The money paid by a store owner to buy goods is called the cost price (C.P.).
    • C.P. = Inventory + Cost of Goods Manufactured

    Selling Price arrow_upward


  • The price at which a store sells the goods is called the selling price (S.P.).
    • S.P. = Cost Price + Profit Margin

    Profit arrow_upward


  • If selling price is more than cost price then it is profit.
    • Profit = Selling Price - Cost Price
  • Profit can be expressed either
    • In dollars
    • In percentage of the cost price

  • Profit is also mentioned in terms of sales price.

  • S.P. and C.P. can be calculated from Profit.


    • Loss arrow_upward


  • If selling price is less than cost price then it is loss.
    • Loss = Cost Price – Selling Price
  • Loss can also be expressed either
    • In dollars
    • In percentage of the cost price

  • S.P. and C.P. can be calculated from Loss


    • Simple Interest arrow_upward


  • Interest paid only on the principal of a loan or on borrowed money.

    • Formula for Simple Interest:

  • Where,
    • S.I. = ‘Simple Interest’ which is the total amount of interest paid.
    • P = ‘Principal' which is the amount lent or borrowed.
    • R = ‘Rate’ which is the percentage of the principal charged as interest each year.
    • If A denotes amount then,

           A = P + I


    Example:

  • Calculate the simple interest when,
    • Principal = $1000
    • Rate = 5%
    • Time = 2 years

    Solution:

    = 100

  • Simple Interest = $100

    • Compound Interest arrow_upward


  • Compound interest is paid at regular intervals on the:
    • Original principal,
    • The accumulated past interest.
  • Compounding of interest allows a principal amount to grow at a faster rate than simple interest.
  • It is calculated as a percentage of only the principal amount.


    • Formula for Compound Interest:

  • When the interest is compounded yearly

    •      A(t) = P(1 + r)t

  • Where,
    • A(t) = Amount after t years.
    • P = Principal (the initial amount you borrow or deposit).
    • r = Annual rate of interest (percentage).
    • t = Number of years the amount is deposited or borrowed for.
    • A is the amount of money accumulated after t years, including interest.

    Example:

  • If $800 is invested at 7% for 6 years. Find the simple interest and the interest compounded annually?

    • Solution:

  • Simple interest:

    •     = PRT = $800 × 0.07 × 6 = $336

  • Compound interest:

    •     A = P (1 + r) n

        = $800 (1.07)6

        = $1200.58

         I = A - P = $1200.58 - $800

           = $400.58


    Interest Compounded n Times Per Year arrow_upward


  • Where,
    • A(t) = Final amount after t years.
    • P = Principal amount (initial investment).
    • r = Annual nominal interest rate (as a decimal).
    • n = Number of times the interest is compounded per year.
    • t = Number of years.

    Frequent Compounding of Interest arrow_upward



    Period

    Interest Credited

    Times Credited per year

    Rate per compounding period

    Annual

    Year

    1

    R

    Semiannual

    6 months

    2

    R/2

    Quarterly

    Quarter

    4

    R/4

    Monthly

    Month

    12

    R/12



    Example:

  • $32000 is invested at 10% for 2 years. Find the interest compounded yearly, semiannually, quarterly, and monthly?

    • Solution:

  • Yearly
    • A = P(1 + r)n = $32000(1.10)2 = $38720
    • I = A - P = $38720 - $32000 = $6720
  • Semiannually:
    • A = P(1 + r/2)2n

          = $32000(1.05)4 = $38896.20

    • I = A - P

          = $38896.20 - $32000

          = $6896.20

  • Quarterly:
    • A = P(1 + r/4)4n

           = $32000(1.025)8

           = $38988.89

    • I = A - P = $38988.89 - $32000 = $6988.89
  • Monthly:
    • r
    • A = P(1 + r)n = $32000(1.00833)24 = $39052.20
    • I = A - P = $39052.20 - $32000 = $7052.20

    Daily Compound Interest Formula arrow_upward


  • Divide r by 365 and multiply n by 365.

  • Where,
    • A(t) = Final amount,
    • P = Principal,
    • r = Annual nominal interest rate,
    • t = Number of years.

    Example:

  • Find the compound amount if $2900 is deposited at 5% interest for 10 years, interest is compounded daily?

    • Solution:

    = $4781.13



    Thank You from Kimavi arrow_upward


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