Question

You go to the cash palace and take out a payday loan. you borrow 1500.00 and will make 25 total payments of 109.41 one every other week for a year. what is the effective annual rate of interest on this loan?

Answer 1

The annualized interest rate is 274.44%

	Interest rate	274.44%
WEEK	Cashflow	Interest	To Principle	Principle
0	$ -1,500.00			$ 1,500.00
2	$      109.41	$    79.17	$       30.24	$ 1,469.76
4	$      109.41	$    77.57	$       31.84	$ 1,437.91
6	$      109.41	$    75.89	$       33.52	$ 1,404.39
8	$      109.41	$    74.12	$       35.29	$ 1,369.10
10	$      109.41	$    72.26	$       37.15	$ 1,331.95
12	$      109.41	$    70.30	$       39.11	$ 1,292.84
14	$      109.41	$    68.23	$       41.18	$ 1,251.66
16	$      109.41	$    66.06	$       43.35	$ 1,208.31
18	$      109.41	$    63.77	$       45.64	$ 1,162.67
20	$      109.41	$    61.36	$       48.05	$ 1,114.62
22	$      109.41	$    58.83	$       50.58	$ 1,064.04
24	$      109.41	$    56.16	$       53.25	$ 1,010.78
26	$      109.41	$    53.35	$       56.06	$     954.72
28	$      109.41	$    50.39	$       59.02	$     895.69
30	$      109.41	$    47.27	$       62.14	$     833.56
32	$      109.41	$    43.99	$       65.42	$     768.14
34	$      109.41	$    40.54	$       68.87	$     699.27
36	$      109.41	$    36.91	$       72.50	$     626.76
38	$      109.41	$    33.08	$       76.33	$     550.43
40	$      109.41	$    29.05	$       80.36	$     470.07
42	$      109.41	$    24.81	$       84.60	$     385.47
44	$      109.41	$    20.34	$       89.07	$     296.41
46	$      109.41	$    15.64	$       93.77	$     202.64
48	$      109.41	$    10.69	$       98.72	$     103.93
50	$      109.41	$      5.48	$     103.93	$ 0.00

Formulas:

	Interest rate	2.74439982938571
WEEK	Cashflow	Interest	To Principle	Principle
0	-1500			=-B4
2	109.41	=E4*$C$1/52	=B5-C5	=E4-D5
4	109.41	=E5*$C$1/52	=B6-C6	=E5-D6
6	109.41	=E6*$C$1/52	=B7-C7	=E6-D7
8	109.41	=E7*$C$1/52	=B8-C8	=E7-D8
10	109.41	=E8*$C$1/52	=B9-C9	=E8-D9
12	109.41	=E9*$C$1/52	=B10-C10	=E9-D10
14	109.41	=E10*$C$1/52	=B11-C11	=E10-D11
16	109.41	=E11*$C$1/52	=B12-C12	=E11-D12
18	109.41	=E12*$C$1/52	=B13-C13	=E12-D13
20	109.41	=E13*$C$1/52	=B14-C14	=E13-D14
22	109.41	=E14*$C$1/52	=B15-C15	=E14-D15
24	109.41	=E15*$C$1/52	=B16-C16	=E15-D16
26	109.41	=E16*$C$1/52	=B17-C17	=E16-D17
28	109.41	=E17*$C$1/52	=B18-C18	=E17-D18
30	109.41	=E18*$C$1/52	=B19-C19	=E18-D19
32	109.41	=E19*$C$1/52	=B20-C20	=E19-D20
34	109.41	=E20*$C$1/52	=B21-C21	=E20-D21
36	109.41	=E21*$C$1/52	=B22-C22	=E21-D22
38	109.41	=E22*$C$1/52	=B23-C23	=E22-D23
40	109.41	=E23*$C$1/52	=B24-C24	=E23-D24
42	109.41	=E24*$C$1/52	=B25-C25	=E24-D25
44	109.41	=E25*$C$1/52	=B26-C26	=E25-D26
46	109.41	=E26*$C$1/52	=B27-C27	=E26-D27
48	109.41	=E27*$C$1/52	=B28-C28	=E27-D28
50	109.41	=E28*$C$1/52	=B29-C29	=E28-D29

Was solved using Goal seek in Excel