Question

Lori has a loan of 80,000 to be paid in 20 level annual payments. The interest and the principal repayment in the 13th payment are equal. Find the amount of principal repaid in the 6th payment.

Answer 1

By trial & error method values at which interest & principal are equal is where

Interest rate = 9.05%

Repayment installment = 8,794.97

	Opening balance	Interest	Installment	Principal repaid	Closing balance
1	80,000.00	7,240.00	8,794.97	1,554.97	78,445.04
2	78,445.04	7,099.28	8,794.97	1,695.69	76,749.35
3	76,749.35	6,945.82	8,794.97	1,849.15	74,900.20
4	74,900.20	6,778.47	8,794.97	2,016.50	72,883.70
5	72,883.70	6,595.97	8,794.97	2,198.99	70,684.71
6	70,684.71	6,396.97	8,794.97	2,398.00	68,286.71
7	68,286.71	6,179.95	8,794.97	2,615.02	65,671.69
8	65,671.69	5,943.29	8,794.97	2,851.68	62,820.02
9	62,820.02	5,685.21	8,794.97	3,109.75	59,710.26
10	59,710.26	5,403.78	8,794.97	3,391.19	56,319.08
11	56,319.08	5,096.88	8,794.97	3,698.09	52,620.99
12	52,620.99	4,762.20	8,794.97	4,032.77	48,588.22
13	48,588.22	4,397.23	8,794.97	4,397.73	44,190.49
14	44,190.49	3,999.24	8,794.97	4,795.73	39,394.76
15	39,394.76	3,565.23	8,794.97	5,229.74	34,165.03
16	34,165.03	3,091.93	8,794.97	5,703.03	28,462.00
17	28,462.00	2,575.81	8,794.97	6,219.15	22,242.84
18	22,242.84	2,012.98	8,794.97	6,781.99	15,460.85
19	15,460.85	1,399.21	8,794.97	7,395.76	8,065.10
20	8,065.10	729.89	8,794.97	8,065.07	0.02

13th Installment covers

4,397.23 for Interest &

4,397.73 for Principal

And as we can see Principal repaid in 6th payment is 2,398

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Answer 2

sy DATE PAGE Joan amount & Rs. 80,000 Installment he X T We know, e non value of a Prisent of Inflow outflow 80,000 X(1 - 11+7)0) Loan outstanding at the end of Be year 3... 13 ly... --b20 Installment x Internt how i Outstandanding amount y - (1+) capital Installment Internet D a X- XII-(1+1)** ) X(1-(1+1)**) GOOD WRITE Wate

we have DATE PAGE We know an 8th payment ant - Capital X11- €1+1) ?) - Y t761+) "? 2X114847) - À Attil X - XQ1+1) 8. X- X(1-C1+1)-8) X - X1 + ) , x + X1 )-3 V - X (148) * = X1+)8 By het and trial 1. vol 1-211 til 0.0669. 1 0.09 1-2(+1) 8 -0,003 by using interpolation 12 . 0+0.0669 -0.003 - 0.0669 0.09-0.1 12 10957 6 0904 29 - GOOD WRITE fx-82 ES PLUS BLEUPAM

DATE CO PAGE intenst sale 0297 0.090429. Istallment X 80,000 to . 8790.525 Joan oulitanding at the end of 6th year. 8790.525 (1-1.0904 29 15 1 1 0.090429 Installment 8990.525 • 70678.59 intent capital. 6391.394 2399.13) GOOD WRITE