05_Chapter10_AppC

05_Chapter10_AppC - BUS 214 Financial Accounting Compound...

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1 CompoundInterest BUS 214, Financial Accounting Compound Interest Compound interest principles are utilized in all types of investing and borrowing activities. The term compound interest is use to indicate that interest is computed on interest. The term simple interest is used when interest is not computed on interest. Compound interest is usually used with long-term financial instruments. Simple interest is commonly used with short-term financial instruments. When dealing with compound interest, it is useful to classify the topic by the type of problem that is being solved. The following outline summarizes the six types of problems that are encountered when dealing with compound interest. In this outline, "P", "F" and "A" are used as follows: "P" is used to represent Present value, "F" is used to represent Future value, and "A" is used to represent a periodic Annuity. The six compound interest problems are: 1. Given "P", find "F" In graphical terms, the problem is: 0 1 2 n-1 n |----------------|----------------|------------- -------------|----------------| P ---------------------- -----------------> F? In terms of notation, the problem is: F = P(F/P,n,i) In algebraic terms, the problem is: F = P x (1 + i) n 2. Given "F", find "P" In graphical terms, the problem is: 0 1 2 n-1 n |----------------|----------------|------------- -------------|----------------| P? <-------------------- ---------------------- F In terms of notation, the problem is: P = F(P/F,n,i) In algebraic terms, the problem is: P = F x 1/(1 + i) n
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2 CompoundInterest 3. Given "F", find "A" In graphical terms, the problem is: 0 1 2 n-1 n |----------------|----------------|------------- -------------|----------------| F < < < < A? A? A? A? In terms of notation, the problem is: A = F(A/F,n,i) In algebraic terms, the problem is: A = F x i/[(1 + i) - 1] n 4. Given "A", find "F" In graphical terms, the problem is: 0 1 2 n-1 n |----------------|----------------|------------- -------------|----------------| A A A A > > > > F? In terms of notation, the problem is: F = A(F/A,n,i) In algebraic terms, the problem is: F = A x [(1 + i) - 1]/i n 5. Given "P", find "A" In graphical terms, the problem is: 0 1 2 n-1 n |----------------|----------------|------------- -------------|----------------| P > > > > A? A? A? A? In terms of notation, the problem is: A = P(A/P,n,i)
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3 CompoundInterest In algebraic terms, the problem is: A = P x i(1 + i) /[(1 + i) - 1] n n 6. Given "A", find "P" In graphical terms, the problem is: 0 1 2 n-1 n |----------------|----------------|------------- -------------|----------------| A A A A P? < < < < In terms of notation, the problem is: P = A(P/A,n,i) In algebraic terms, the problem is: P = A x [(1 + i) - 1]/i(1 + i) n n
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1 CompInterestEx BUS 214, Financial Accounting Compound Interest Exercise Part 1 Assume in each of the following problems that the applicable interest rate is 10%. Some compound interest factors are: (F/P,10,10%) = 1 x (1 + 10%) = 2.59374246 10 (P/F,10,10% = 1 x [1/(1 + 10%) ] = 0.38554329 10 (A/F,10,10%) = 1 x {10%/[(1 + 10%) - 1]} = 0.06274539 10 (F/A,10,10%) = 1 x{ [(1 + 10%) - 1]/10%} = 15.93742460 10 (A/P,10,10%) = 1 x {10%(1 + 10%) /[(1 + 10%) - 1]} = 0.16274539 10 10 (P/A,10,10%) = 1 x {[(1 + 10%) - 1]/10%(1 + 10%) } = 6.14456711 10 10 Problem 1: If $10,000 is invested now, what will be the value of the investment in 10 years? Graphical representation 0 1 2 9 10 |----------------|----------------|------------- -------------|----------------| Numeric solution Problem 2: How much must be invested now to have $25,937 in 10 years? Graphical representation 0 1 2 9 10 |----------------|----------------|------------- -------------|----------------| Numeric solution
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2 CompInterestEx Problem 3: What uniform amount must be deposited in an account at the end of each year for 10 years if the account is to contain $60,000 at the end of that period? Graphical representation 0 1 2 9 10 |----------------|----------------|------------- -------------|----------------| Numeric solution Problem 4: If an investment of $3,765 is made at the end of each year for 10 years, how much will be accumulated by the end of the 10th year?
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