1090 60 r r 1 1 1 23 solve for r on a financial

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if the present value were $1090 and there are 23 months of $60 payments. => $1090 = $60 * ] r ) r 1 ( 1 1 [ 23 + - ; solve for r on a financial calculator as follows: N = 23, PV = $1090, PMT = -$60; compute I; I = 2.0632% per month, Convert to an E.A.R.: (1.020632) 12 –1 = 27.77% 4. There are several ways to solve this problem. First, you can use brute force and discount all the cash flows back individually ( YUCK!). Alternatively, you can see that there are effectively two annuity streams here; a five period ordinary annuity of $253 with the first cash flow one period away and then a four period ordinary annuity of $253 with the first cash flow starting 7 periods from now. Recalling that the annuity present value formula assumes that payments start at the end of the period (i.e., one period away), you can solve the for present value of these cash flows as follows: => PV = $253 * PVIFA(7.9%,5) + 6 ) 079 . 1 ( ) 4 %, 9 . 7 ( * 253 $ PVIFA => = $253 * ] 079 . ) 079 . 1 ( 1 1 [ 5 - + $253 * ] 079 . ) 079 . 1 ( 1 1 [ 4 - * ] ) 079 . 1 ( 1 [ 6 => = $1,012.82 + $532.19 = $1,545.01 On a financial calculator: Step 1: Determine the present value of the first 5 payments: PMT = $253, N = 5, I = 7.9; compute PV = $1,012.82 Step 2: Determine value of the last 4 payments as of t = 6: PMT = $253, N = 4, I = 7.9; compute PV = $839.84 This is the value at the end of 6th year, so you must discount it 6 more years. FV = $839.84, N = 6, I = 7.9; compute PV = $532.19 Step 3: Add the two values together $1,012.82 + $532.19 = $1,545.01 F301 TVM practice set II solutions 2
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Now, a simpler approach. Calculate the value of a 10-year, $253 annuity and then subtract off the present value of the missing payment at t = 6. => PV = $253 * PVIFA(7.9%,10) - $253 * PVIF(7.9%,6) => $253 * ] 079 . ) 079 . 1 ( 1 1 [ 10 - - 6 ) 079 . 1 ( 253 $ => $1,705.33 - $160.32 = $1,545.01 On a financial calculator: Step 1: Determine the present value of a 10 year annuity: PMT = $253, N = 10, I = 7.9; compute PV = $1,705.33 Step 2: Determine the present value of the 6th payment (single CF) that was missed: FV = $253, N = 6, I = 7.9; compute PV = $160.32 Step 3: Take the difference between these two values: $1,705.33 - $160.32 = $1,545.01 5. Fifteen-percent compounded monthly implies a monthly interest rate of .15 / 12 = .
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