# Problem 5At a constant interest rate of 15, compounded annually, .pdf

26. Mar 2023
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### Problem 5At a constant interest rate of 15, compounded annually, .pdf

• 1. Problem 5 At a constant interest rate of 15%, compounded annually, what is the present value of an income stream paying \$50 next quarter and growing at 2% per quarter until the end of the third year? From that point on it grows at 1% per quarter indefinitely. Solution The income grows by 2% for first 12 quarters after which it grows perpetually at 1% per quarter. Interest rate, r = 15% p.a. = 15/4 = 3.75% quarterly The income stream looks as shown below Quarter Income(I) Remarks 1 50.00 2 51.00 2% increase 3 52.02 2% increase 4 53.06 2% increase 5 54.12 2% increase 6 55.20 2% increase 7 56.31 2% increase 8 57.43
• 2. 2% increase 9 58.58 2% increase 10 59.75 2% increase 11 60.95 2% increase 12 62.17 2% increase 13 62.79 1% increase Present Value,PV = I1/(1+r) + I2/(1+r)2 + I3/(1+r)3+ ........ + I12/(1+r)12 + I13/(1+r)13 + .... constant growth So PV = I1/(1+r) + I2/(1+r)2+ I2/(1+r)2+ .........+ I12/(1+r)12+ I13/((1+r)13*(r-g)) {Infinite GP series formula used} where g = 1% or 0.01 So PV = 48.19 + 47.38 + 46.58 + 45.80 + 45.02 + 44.26+ 43.52+ 42.78+ 42.06+41.35+40.65+39.97+1414.87 So Present Value, PV = \$1942.43 Quarter Income(I) Remarks 1 50.00 2 51.00 2% increase 3 52.02 2% increase 4 53.06
• 3. 2% increase 5 54.12 2% increase 6 55.20 2% increase 7 56.31 2% increase 8 57.43 2% increase 9 58.58 2% increase 10 59.75 2% increase 11 60.95 2% increase 12 62.17 2% increase 13 62.79 1% increase