Question

Red Sea Co. obtained a $200,000 loan from ANB bank at 6% annual interest rate that will be paid off in annual payments over ten years. How much will each annual payment be?

Answer 1

Answer.

If present value annuity factor is not given.

Annual payment = [ Principal * r ( 1 + r )10 ] / [ ( 1 + r )10 – 1 ]

Rate (r) = 6% or 0.06

No. of period (n) = 10

Annual payment = [ $ 200,000 * 0.06 ( 1+.06)10 ] / [ (1+0.6)10 – 1 ]

Annual payment = [ $ 12,000 * 1.790848 ] / [ 1.790848 – 1 ]

Annual payment = [ $ 21,490.176 ] / [ 0.790848 ]

Annual payment = $ 27,173.59

[ value of 1.0610 = 1.790848 ]

or

If the table of present value of annuity factor is given we can find annual payment as follows:

Present value of loan = $ 200,000

Present value of annuity factor @ 6 % for 10 year = 7.360

Annual payment = $ 200,000 / 7.3601 = $ 27,173.54

Verification of result:

year	Annual payment	Interest	Principal	Carrying value
.	.	.	.	200,000
1	27173.59	12,000 ( 200,000 *6%)	15,173.59 ( 27173.59 – 12000 )	184,826.41 ( 200,000 - 15,173.59 )
2	27173.59	11,089.58 ( 184,826.41*6%)	16,084.01 ( 27,173.59 – 11,089.58 )	168,742.40 ( 184,826.41 – 16,084.01 )
3	27173.59	10,124.54	17,049.05	151,693.36
4	27173.59	9,101.602	18,071.99	133,621.37
5	27173.59	8,017.282	19,156.31	114,465.06
6	27173.59	6,867.904	20,305.69	94,159.38
7	27173.59	5,649.563	21,524.03	72,635.35
8	27173.59	4,358.121	22,815.47	49,819.88
9	27173.59	2,989.193	24,184.4	25,635.48
10	27173.59	1,538.129	25,635.46	0.02