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Quiz02 - 1 value of a 4 period annuity with payment C = 136...

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1 Answers to Quiz 02 1) q stands for quarterly and s for semiannually. It must be true that the e/ective annual rate must be equal for both APRs (with di/erent compounding frequencies), i.e.: 1 + APR s 2 ± 2 = 1 + APR q 4 ± 4 Hence we get: APR q = 4 1 + APR s 2 ± 2 4 1 ! = 5 : 956% 2) This is just a growing perpetuity with a negative growth rate with C = 100 , g = & 0 : 2 , r = 3% 2 = 0 : 015 , T = 40 : Simply apply the formula: PV = C r g 1 1 + g 1 + r ± T ! = 100 1 0 : 215 1 & 0 : 8 1 : 015 ± 40 ! = 465 : 08 3) First step: Determine the semiannual payment C of the loan: The input variables are: r = 4% 2 = 2% T = 8 PV = 1000 PV = C 1 r 1 1 1 + r ± T ! C = r ± PV 1 ² 1 1+ r ³ T ± = 0 : 02 ± 1000 1 ´ 1 1 : 02 µ 8 = 136 : 51 The Principal reduction in year 3 is simply the di/erence between the bal- ances after period 4 and period 6. After period 4, the balance is just the present

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Unformatted text preview: 1 value of a 4 period annuity with payment C = 136 : 51 : After period 6, the bal-ance is just the present value of a 2 period annuity with payment2 C = 136 : 51 Balance after period 4: B 4 = C 1 r 1 & & 1 1 + r ± 4 ! Balance after period 6: B 6 = C 1 r 1 & & 1 1 + r ± 2 ! Thus, the principal reduction is: B 4 & B 6 = C 1 r 1 & & 1 1 + r ± 4 ! & C 1 r 1 & & 1 1 + r ± 2 ! = C r & 1 1 + r ± 2 & & 1 1 + r ± 4 ! = 254 : 75 2...
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Quiz02 - 1 value of a 4 period annuity with payment C = 136...

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