Question

Brianna borrows $500 on January 1,2015. She repays the loand with 20 annual payments starting January 1, 2016. The payments in even numbered years are y each and the oayments in odd numbered years are x each. If i=.08 and the total of all 20 loan payments is 1,023, find x and y.

Answer 1

Sum of discount factors of odd years

5.10

Sum of discount factors of even years

4.72

10x+10y= 1023

Hence x= (1023-10y)/10

x= 102.3-y

PV of annual payments = 500 = 5.1x+4.72y

500= 5.1*(102.3-y)+4.72y

500 = 521.73-5.1y+4.72y

0.38y=21.73

y= $57.18

x= 102.3-57.18 = 45.12

Workings

Odd Years	Discount factor		Even Years	Discount factor
1	0.93		2	0.86
3	0.79		4	0.74
5	0.68		6	0.63
7	0.58		8	0.54
9	0.50		10	0.46
11	0.43		12	0.40
13	0.37		14	0.34
15	0.32		16	0.29
17	0.27		18	0.25
19	0.23		20	0.21
Sum of discount factors of odd years	5.10		Sum of discount factors of even years	4.72

Book2 - Excel Sign in - . AutoSave off 2 File Home H D . Draw Page Layout Insert Formulas Data Review View Help Tell me what you want to do Share Comment = = = 2 Calibri 11 A A BIU - 2-0-A General $ -% Insert - EX Delete Format Paste - -23 Conditional Format as Formatting Table Styles Cell Styles Sort & Filter Find & Select Clipboard Font Alignment Number Cells Editing X fx Odd Years A B Odd Years Even Years Discount factor =1/1.084B2 =1/1.08 B3 =1/1.08^B4 =1/1.084B5 =1/1.08 B6 =1/1.084B7 =1/1.084B8 =1/1.084B9 =1/1.084B10 =1/1.08 B11 10 Discount factor =1/1.084E2 =1/1.084E3 =1/1.084E4 =1/1.08^E5 =1/1.084E6 =1/1.084E7 =1/1.08AE8 =1/1.084E9 =1/1.084E10 =1/1.08^E11 14 16 18 20 19 Sum of discount factors of odd years Sum of discount factors of even years =SUM(C2:C11) =SUM(F2:F11)