This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: The Theory of Interest  Solutions Manual Chapter 1 1. ( a ) Applying formula (1.1) ( 29 ( 29 2 2 3 and 3 A t t t A = + + = so that ( 29 ( 29 ( 29 ( 29 ( 29 2 1 2 3 . 3 A t A t a t t t k A = = = + + ( b ) The three properties are listed on p. 2. (1) ( 29 ( 29 1 3 1. 3 a = = (2) ( 29 ( 29 1 2 2 0 for 0, 3 a t t t ′ = + ≥ so that ( 29 a t is an increasing function. (3) ( 29 a t is a polynomial and thus is continuous. ( c ) Applying formula (1.2) ( 29 ( 29 [ ] ( 29 ( 29 2 2 2 2 1 2 3 1 2 1 3 2 3 2 1 2 2 3 2 1. n I A n A n n n n n n n n n n n = = + + + + = + + +  + = + 2. ( a ) Appling formula (1.2) ( 29 ( 29 [ ] ( 29 ( 29 [ ] ( 29 ( 29 [ ] ( 29 ( 29 1 2 1 2 1 1 0 . n I I I A A A A A n A n A n A + + + = + + + = K L ( b ) The LHS is the increment in the fund over the n periods, which is entirely attributable to the interest earned. The RHS is the sum of the interest earned during each of the n periods. 3. Using ratio and proportion ( 29 5000 12,153.96 11,575.20 $260 11,130 . = 4. We have ( 29 2 , a t at b = + so that ( 29 ( 29 1 3 9 1.72. a b a a b = = = + = 1 The Theory of Interest  Solutions Manual Chapter 1 Solving two equations in two unknowns .08 and 1. a b = = Thus, ( 29 ( 29 2 5 5 .08 1 3 a = + = ( 29 ( 29 2 10 10 .08 1 9 a = + = . and the answer is ( 29 ( 29 10 9 100 100 300. 5 3 a a = = 5. ( a ) From formula (1.4 b ) and ( 29 100 5 A t t = + ( 29 ( 29 ( 29 5 5 4 125 120 5 1 . 4 120 120 24 A A i A = = = = ( b ) ( 29 ( 29 ( 29 10 10 9 150 145 5 1 . 9 145 145 29 A A i A = = = = 6. ( a ) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 5 4 5 4 100 1.1 and 5 4 100 1.1 1.1 1.1 1 .1. 4 100 1.1 t A t A A i A =  = = = = ( b ) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 10 9 10 9 10 9 100 1.1 1.1 1.1 1 .1. 9 100 1.1 A A i A  = = = = 7. From formula (1.4 b ) ( 29 ( 29 ( 29 1 1 n A n A n i A n = so that ( 29 ( 29 ( 29 1 1 n A n A n i A n = and ( 29 ( 29 ( 29 1 1 . n A n i A n = + 8. We have 5 6 7 .05, .06, .07, i i i = = = and using the result derived in Exercise 7 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 5 6 7 7 4 1 1 1 1000 1.05 1.06 1.07 $1190.91. A A i i i = + + + = = 9. ( a ) Applying formula (1.5) ( 29 615 500 1 2.5 500 1250 i i = + = + so that 2 The Theory of Interest  Solutions Manual Chapter 1 1250 115 and 115/1250 .092, or 9.2%. i i = = = ( b ) Similarly, ( 29 630 500 1 .078 500 39 t t = + = + so that 1 3 39 130 and 130/39 10/3 3 years. t t = = = = 10. We have ( 29 1110 1000 1 1000 1000 it it = + = + 1000 110 and .11 it it = = so that ( 29 ( 29 [ ] ( 29 ( 29 [ ] 3 500 1 2 500 1 1.5 4 500 1 1.5 .11 $582.50. i t it + = + = + = 11. Applying formula (1.6) ( 29 ( 29 .04 and .025 1 1 1 .04 1 n i i i n n = = + + so that ( 29 .025 .001 1 .04, .001 .016, and 16 . n n n + = = = 12. We have 1 2 3 4 5 .01 .02 .03 .04 .05 i i i i i = = = = = and adapting formula (1.5) ( 29 ( 29 1 2 3 4 5 1000 1 1000 1.15 $1150. i i i i i + + + + + = =...
View
Full
Document
This document was uploaded on 12/10/2011.
 Fall '09

Click to edit the document details