Question

Problem 3

At an annual percentage rate (APR) of 16%, compounded quarterly, what is the present value of an income stream specified as follows? It pays $60 next quarter and grows at 2% per quarter until the end of the third year, and from that point on it grows at 1% per quarter indefinitely

Answer 1

- 100 101 Formatting Styles 2 Clear Format Painter Clipboard A B as Table Styles Font D Alignment H C Filter Editing R E F G I Number K J L M N Cells P O Q Quarterly rate 4.00% o 1 Year S Cash flow PV 60.00 57.69 Year 1 2 61.20 56.58 3 62.42 55.49 4 63.67 54.43 5 64.95 53.38 Year 2 6 66.24 52.35 67.57 51.35 8 68.92 50.36 70.30 49.39 Year 3 9 10 71.71 4 8.44 11 73.14 47.51 12 74.60 46.60 13 75.35 1568.75 2192.33

A C D E F G I J K L M N O P Q 2 Quarterly -16%/4 Year 1 Year 2 Year 3 Year 01 2 3 8 10 11 12 Cash flow 60 =E6*1.02 =F6*1.02 =G61.02 =H6*1.02 =16*1.02 =J6*1.02 +K6*1.02 =L6*1.02 =M6*1.02 =N6*1.02 =06*1.02 =P6*1.01 PV =E6/(1+$E$2) "E5 =F6/(1+$E$2)^F5 =G6/(1+$E$2)^G5 =H6/(1+$E$2)^H5 =16/(1+$E$2)^15 = 36/(1+$E$2)^5 =K6/(1+$E$2)^K5 =L6/(1+$E$2)^L5 =M6/(1+$E$2)^M5 =N6/(1+$E$2)^N5 =06/(1+$E$2)^05 =P6/(1+$E$2)^P5 =Q6/((E2-1%)*(1+E2)^12) 10 PV =SUM(E7:07)