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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 3month 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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 Fall '09

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