Chapter003

Chapter003 - The Theory of Interest - Solutions Manual...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
The Theory of Interest - Solutions Manual 23 Chapter 3 1. The equation of value using a comparison date at time 20 t = is 20 10 50,000 1000 at 7%. sX s = + Thus, 20 10 50,000 1000 50,000 40,995.49 $651.72. 13.81645 s X s == = 2. The down payment ( D ) plus the amount of the loan ( L ) must equal the total price paid for the automobile. The monthly rate of interest is .18/12 .015 j = = and the amount of the loan ( L ) is the present value of the payments, i.e. ( ) 48 .015 250 250 34.04255 8510.64. La = Thus, the down payment needed will be 10,000 8510.64 $1489.36. D =− = 3. The monthly interest rate on the first loan ( L 1 ) is 1 .06/12 .005 j = = and ( )( ) 1 48 .005 500 500 42.58032 21,290.16. = The monthly interest rate on the second loan ( L 2 ) is 2 .075/12 .00625 j = = and 21 25,000 25,000 21,290.16 3709.84. LL = The payment on the second loan ( R ) can be determined from 12 .00625 3709.84 Ra = giving 3709.84 $321.86. 11.52639 R 4. A’s loan: 8 .085 20,000 Ra = 20,000 3546.61 5.639183 R so that the total interest would be ( )( ) 8 3546.61 20,000 8372.88. −= B’s loan: The annual interest is ( ) ( ) .085 20,000 1700.00 = so that the total interest would be ) 8 1700.00 13,600.00. = Thus, the difference is 13,600.00 8372.88 $5227.12. =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Theory of Interest - Solutions Manual Chapter 3 24 5. Using formula (3.2), the present value is () 11 1 where . n n n i na i in ⎡⎤ −+ ⎣⎦ == This expression then becomes 2 1 1 1. 1 1 n n n n n n n n n + ⎛⎞ ⎢⎥ ⎜⎟ ⎝⎠ =− + 6. We are given 1 , n n v ax i s o t h a t n vi x = Also, we are given 2 2 1 , n n v ay i so that 2 n y = But 2 2 nn vv = so that 2 . iy ix −=− This equation is the quadratic ( ) 22 20 x ix y i −= so that 2 2 . x y i x = Then applying formula (1.15a), we have 2 2 . 12 y d x y + +− 7. We know that 1, dv and directly applying formula (3.8), we have 88 8 8 1 1 . 9 5.695. .1 vd a dd −− = = ±± 8. The semiannual interest rate is .06/ 2 .03. j = = The present value of the payments is ( ) ( ) 21 9 100 100 15.87747 8.01969 $2389.72. aa += + = 9. We will use a comparison date at the point where the interest rate changes. The equation of value at age 65 is 25 .08 15 .07 3000 sR a = so that 25 .08 15 .07 3000 236,863.25 $24,305 9.74547 s R a = to the nearest dollar. 10. ( a ) Using formulas (3.1) and (3.7) ( ) 21 2 1 . n n n n av v v v v a v =++ ++ + − =+++ + + " "
Background image of page 2
The Theory of Interest - Solutions Manual Chapter 3 25 ( b ) Using formulas (3.3) and (3.9) () 1 1 11 1 1 1 1 1 1 11 . nn n n n s i i i i i i i ⎡⎤ =++ + + + ++ ⎣⎦ =+ + + + + + +− =− + + ±± " " ( c ) Each formula can be explained from the above derivations by putting the annuity-immediate payments on a time diagram and adjusting the beginning and end of the series of payments to turn each into an annuity-due. 11. We know that 1 and . q p pq i v ax sy di + == Thus, 1 1 p vd x i v x =− =− and , q ii y + so that 1 1. q v i y Finally, 1 1 1 .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/18/2010 for the course MATH 320 taught by Professor Dr.k during the Spring '10 term at Nevada.

Page1 / 11

Chapter003 - The Theory of Interest - Solutions Manual...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online