MA373 F15 Homework Chapter 4 Solutions

MA373 F15 Homework Chapter 4 Solutions - Math 373 Fall 2013...

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October 3, 2015 Copyright 2013, 2014, 2015 Math 373 Fall 2013 Homework Chapter 4 Chapter 4 Section 5 1. A 30 year annuity immediate pays 50 each quarter of the first year. It pays 100 each quarter of the second year. The payments continue to increase annually so that the payments in each quarter are 50 higher than the previous year. a. Calculate the present value of this annuity at an annual effective interest rate of 10%. Solution: Use the formula that doesn’t follow the rules (4) 0.25 30 30 ( ) ( ) ( ) 30 0.1 (1.1) 1 0.024113689 4 50 1 1.1 (1.1) 30 1.1 0.1 ( ) 50 50 17,936.59 0.024113689 n n i i m ni ni m m n n i i FirstPayment a nv a nv Ia i i m b. Calculate the present value of this annuity at a nominal rate of 10% compounded quarterly. Solution: Now we need to redefine our interest rates: (4) (4) 4 0.1 0.025 4 (1 ) (1.025) 1.103812891 0.103812891 i i i i Then use the formula as we did in part a.
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October 3, 2015 Copyright 2013, 2014, 2015 30 30 ( ) ( ) ( ) 30 50 1 1.1038 (1.1038) 30 1.1038 0.1038 ( ) 50 50 17,067.43 0.025 n n i i m ni ni m m n n FirstPayment a nv a nv Ia i i m 2. An annuity due makes monthly payments for 15 years. The first payment is 10. Each subsequent payment is 10 larger than the previous payment. In other words, the payment at the start of the second month is 20 and the payment at the start of the third month is 30, etc. Calculate the present value of this annuity using a nominal interest rate of 12% compounded monthly. Solution: Now we need to use the “P and Q” formula from our notes. Be careful to use the correct interest rate! (12) (12) . , 180 180 180 (12) 10; 10; 12*15 180 0.01 12 ( ) 1 ( ) 12 1 1.01 1 1.01 10 1.01 ( ) 1.01 10 180 1.01 54,675 0.01 0.01 0.01 12 P Q P Q n n n n n P Q n i i PV I a I a Q Pa a nv i
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