1. The total interest paid by First Simple Bank is the interest rate per period times the number of periods. In other words, the interest by First Simple Bank paid over 10 years will be: .058(10) = .58 First Complex Bank pays compound interest, so the interest paid by this bank will be the FV factor of $1, or: (1 + r) 10 Setting the two equal, we get: (.058)(10) = (1 + r) 10 1 r = 1.581/10 1 r = .0468, or 4.68%

2. For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m)]m 1 So, for each bank, the EAR is: First National: EAR = [1 + (.101 / 12)]12 1 = .1058, or 10.58% First United: EAR = [1 + (.103 / 2)]2 1 = .1057, or 10.57% For a borrower, First United would be preferred since the EAR of the loan is lower. Notice that the higher APR does not necessarily mean the higher EAR. The number of compounding periods within a year will also affect the EAR.

3. The APR is simply the interest rate per period times the number of periods in a year. In this case, the interest rate is 13.7 percent per month, and there are 12 months in a year, so we get: APR = 12(13.7%) APR = 164.40% To find the EAR, we use the EAR formula: EAR = [1 + (APR / m)]m 1 EAR = (1 + .137) 12 1 EAR = 3.6679, or 366.79%Notice that we didnt 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.

4. The time line is: 0 1 60 $58,600 C C C C C C C C C We need to use the PVA(present value of annuity) due equation, which is: PVAdue = (1 + r)PVA Using this equation: PVAdue = $58,600 = [1 + (.052 / 12)] C[{1 1 / [1 + (.052 / 12)]60]} / (.052 / 12) $58,347.16 = $C{1 [1 / (1 + .052 / 12)60]} / (.052 / 12) C = $1,106.44 Notice, to find the payment for the PVA due, we find the PV of an ordinary annuity, then compound this amount forward one period.

5. Here, we have two cash flow streams that will be combined in the future. In essence, we have three time lines. We will start with the time lines for the savings period, which are: Bond account: 0 1 2 3 4 5 6 7 8 9 10 $75,000 $6,000 $6,000 $6,000 $6,000 $6,000 $6,000 $6,000 $6,000 $6,000 $6,000 Stock account: 0 10 $300,000 To find the withdrawal amount, we need to know the present value, as well as the interest rate and periods, which are given. The present value of the retirement account is the future value of the stock and bond account. We need to find the future value of each account and add the future values together. For the bond account the future value is the value of the current savings plus the value of the annual deposits. So, the future value of the bond account will be: FV = C{[(1 + r) t 1] / r} + PV(1 + r) tFV = $6,000{[(1 + .07)10 1] / .07} + $75,000(1 + .07)10 FV = $230,435.04 The total value of the stock account at retirement will be the future value of a lump sum, so: FV = PV(1 + r) t FV = $300,000(1 + .105)10 FV = $814,224.25 The total value of the account at retirement will be: Total value at retirement = $230,435.04 + 814,224.25 Total value at retirement = $1,044,659.29 So, at retirement, we have: 0 1 25 $1,044,659.29 C C C C C C C C C This amount is the present value of the annual withdrawals. Now we can use the present value of an annuity equation to find the annuity amount. Doing so, we find the annual withdrawal will be: PVA = C({1 [1 / (1 + r) t ]} / r)) $1,044,659.29 = C[{1 [1 / (1 + .0625)]25} / .0625] C = $83,671.59

6. Here, we are finding the price of annual coupon bonds for various maturity lengths. The bond price equation is: PVIF r%, n (Present value Interst factor, 1/(1+r)^n) PVIFA r%, n (present value interest factor of annuity, (1- 1/(1+r)^n) / r) P = C(PVIFAR%,t) + $1,000(PVIFR%,t) X: P0 = $42.50(PVIFA3.5%,13) + $1,000(PVIF3.5%,13) = $1,126.68 P1 = $42.50(PVIFA3.5%,12) + $1,000(PVIF3.5%,12) = $1,120.44 P3 = $42.50(PVIFA3.5%,10) + $1,000(PVIF3.5%,10) = $1,106.59 P8 = $42.50(PVIFA3.5%,5) + $1,000(PVIF3.5%,5) = $1,062.37 P12 = $42.50(PVIFA3.5%,1) + $1,000(PVIF3.5%,1) = $1,014.25 P13 = $1,000 Y: P0 = $35(PVIFA4.25%,13) + $1,000(PVIF4.25%,13) = $883.33 P1 = $35(PVIFA4.25%,12) + $1,000(PVIF4.25%,12) = $888.52 P3 = $35(PVIFA4.25%,10) + $1,000(PVIF4.25%,10) = $900.29 P8 = $35(PVIFA4.25%,5) + $1,000(PVIF4.25%,5) = $939.92 P12 = $35(PVIFA4.25%,1) + $1,000(PVIF4.25%,1) = $985.90P13 = $1,000 All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called pull to par. In both cases, the largest percentage price changes occur at the shortest maturity lengths. Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately. This is because we calculate the clean price of the bond.

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