Chapter004

# Chapter004 - The Theory of Interest Solutions Manual...

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Unformatted text preview: The Theory of Interest - Solutions Manual Chapter 4 1. The nominal rate of interest convertible once every two years is j , so that ( 29 4 4 .07 1 1 and 1.035 1 .14752. 2 j j + = + =- = ÷ The accumulated value is taken 4 years after the last payment is made, so that ( 29 ( 29 ( 29 2 8 2000 1 2000 13.60268 1.31680 \$35,824 to the nearest dollar. j s j + = = 2. The quarterly rate of interest j is obtained from ( 29 4 1 1.12 so that .02874. j j + = = The present value is given by ( 29 ( 29 40 20 600 200 600 24.27195 200 15.48522 \$11,466 to the nearest dollar. j j a a- =- = && && 3. The equation of value at time 8 t = is ( 29 ( 29 ( 29 ( 29 [ ] 100 1 8 1 6 1 4 1 2 520 i i i i + + + + + + + = so that 4 20 5.2, or 20 1.2, and .06, or 6%. i i i + = = = 4. Let the quarterly rate of interest be j . We have 40 40 400 10,000 or 25. j j a a = = Using the financial calculator to find an unknown j , set N 40 PV 25 PMT 1 = = = - and CPT I to obtain .02524, j = or 2.524%. Then ( 29 ( 29 ( 29 12 12 4 12 1 1.02524 and .100, or 10.0%. 12 i i + = = ÷ 5. Adapting formula (4.2) we have ( 29 ( 29 ( 29 8 32 .035 4 .035 2000 1.035 57.33450 2000 1.31681 \$35,824 to the nearest dollar. 4.21494 s s = = ÷ 34 The Theory of Interest - Solutions Manual Chapter 4 6. ( a ) We use the technique developed in Section 3.4 that puts in imaginary payments and then subtracts them out, together with adapting formula (4.1), to obtain ( 29 176 32 4 200 . a a s- Note that the number of payments is 176 32 36, 4- = which checks. ( b ) Similar to part ( a ), but adapting formula (4.3) rather than (4.1), we obtain ( 29 180 36 4 200 . a a a- Again we have the check that 180 36 36. 4- = 7. The monthly rate of discount is ( 29 12 .09 .0075 12 12 j d d = = = and the monthly discount factor is 1 .9925. j j v d = - = From first principles, the present value is ( 29 ( 29 ( 29 ( 29 ( 29 120 6 12 114 6 1 .9925 300 1 .9925 .9925 .9925 300 1 .9925- + + + + = - L upon summing the geometric progression. 8. Using first principles and summing an infinite geometric progression, we have ( 29 3 3 6 9 3 3 1 125 1 91 1 1 v v v v v i + + + = = =- +- K and ( 29 ( 29 3 3 91 216 1 1 or 1 125 125 i i +- = + = 1 3 216 6 and 1 1.2 which gives .20, or 20%. 125 5 i i + = = = = ÷ 9. Using first principles with formula (1.31), we have the present value [ ] .02 .04 .38 100 1 e e e--- + + + + L and summing the geometric progression .4 .02 1 100 . 1 e e---- 35 The Theory of Interest - Solutions Manual Chapter 4 10. This is an unusual situation in which each payment does not contain an integral number of interest conversion periods. However, we again use first principles measuring time in 3-month periods to obtain 8 140 4 3 3 3 1 v v v + + + + L and summing the geometric progression, we have 4 3 48 1 ....
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Chapter004 - The Theory of Interest Solutions Manual...

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