Ch_5_Part_2 - BAC1644 Tutorial Chapter 5 Part 2 12 For...

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BAC1644 Tutorial Chapter 5 Part 2 12. For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m )] m 1 EAR = [1 + (.08 / 4)] 4 1 = .0824 or 8.24% EAR = [1 + (.18 / 12)] 12 1 = .1956 or 19.56% EAR = [1 + (.14 / 365)] 365 1 = .1502 or 15.02% EAR = [1 + (.12 / 2)] 2 1 = .1236 or 12.36% 13. Here we are given the EAR and need to find the APR. Using the equation for discrete compounding: EAR = [1 + (APR / m )] m 1 We can now solve for the APR. Doing so, we get: APR = m [(1 + EAR) 1/ m 1] EAR = .12 = [1 + (APR / 2)] 2 1 APR = 2[(1.12) 1/2 1] = 11.66% EAR = .08 = [1 + (APR / 12)] 12 1 APR = 12[(1.08) 1/12 1] = 7.72% EAR = .13 = [1 + (APR / 52)] 52 1 APR = 52[(1.13) 1/52 1] = 12.24% EAR = .11 = [1 + (APR / 365)] 365 1 APR = 365[(1.11) 1/365 1] = 10.44% 19. The APR is simply the interest rate per period times the number of periods in a year. In this case, the interest rate is 15 percent per month, and there are 12 months in a year, so we get: APR = 12(15%) APR = 180% To find the EAR, we use the EAR formula: EAR = [1 + (APR / m )] m 1 EAR = (1 + .15) 12 1 EAR = 4.3503 or 435.03% Notice that we didn’t need to divide the APR by the number of compounding periods per year. We do this division to get the interest rate per period, but in this problem we are already given the interest rate per period. 20. We first need to find the annuity payment. We have the PVA, the length of the annuity, and the interest rate. Using the PVA equation: PVA = C ({1 – [1/(1 + r ) t ]} / r )
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BAC1644 Tutorial Chapter 5 Part 2 $73,800 = $ C [1 {1 / [1 + (.061/12)] 60 } / (.061/12)] Solving for the payment, we get: C = $73,800 / 51.6014 C = $1,430.20 To find the EAR, we use the EAR equation: EAR = [1 + (APR / m )] m 1 EAR = [1 + (.061 / 12)] 12 1 EAR = .0627 or 6.27% 21. Here we need to find the length of an annuity. We know the interest rate, the PV, and the payments.
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This note was uploaded on 01/14/2012 for the course ACCOUNT 102 taught by Professor Adams during the Spring '11 term at Bradford School of Business.

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Ch_5_Part_2 - BAC1644 Tutorial Chapter 5 Part 2 12 For...

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