ma305_may_2002_exam_solutions_slides

# ma305_may_2002_exam_solutions_slides - COMPOUND INTEREST...

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1 COMPOUND INTEREST EXAM PAPER May 2002 a) b) c) d) e) f) ( ) ( ) ( ) 10 10 (12) (12) 10 10 (4) (4) 10 10 10 10 10 10 10 10 10 1.029709 7.3601 7.57876 1.032211 13.1808 13.60537 100 100 100 1728.70 0.057847 10 38.0614 10 34.2354 10(1 ) i a a i s s d a d a v Ia a v Ia i s Ds δ = = × = = = × = = = = - = = - = = + - = 83.5224 d = a) b) c) d) => d) gives the highest annual effective rate of interest 4 (4) (4) 0.06 12 (12) (12) 1 0.06 1 1 0.062319 4 0.06 1 0.06184 0.06 1 1 0.06168 12 0.06 (1 ) 1 0.063829 d d i i e i i i d i d - - = = - - = = = - = = = + - = = = - - = 96 20 1 500(1.0075) £2,572.93 (1 0.045) × = -

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2 [ ] 5 5 5 5 5 0 0 5 5 0 0 5 5 0 0 1 exp exp[ln(1 )] 1 6 exp[ln6 ln(1 )] exp ln 1 6 6 ln(1 ) 10.75 1 t t s ds dt s dt s t dt dt t dt s t = = + + = - + = + = = + = + APR is the effective rate of interest i rounded to lower 1/10 of 1%. Therefore i is given by:- at 15% at 20% hence APR=18.7% 2 2 2000 1289.29 1.55124 a a = = 2 2 1.6257 1.5278 .1875 a a i = = = (2) (2)@8% @3.92305% 5 9 9 9 0.08 0.0392305 2 2 200 10( ) 400 1.059615 3.9927 1692.29 9 7.7541 9 .707283 10 10 353.95 .0392305 £2,046.24 i i pv a Ia A B A a v B i A B = = = × + = + = × × = - - × = = = + = a) • A preference share pays a dividend which is generally
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## ma305_may_2002_exam_solutions_slides - COMPOUND INTEREST...

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