In January 2018 Ms Langa took a loan of R250 000 that matures in December 2033....

In January 2018 Ms Langa took a loan of R250 000 that matures in December 2033. The bank charges an interest rate of 24% and requires her to repay in equal semi-annual instalments over the period.

b. What is the number of repayments expected to complete the schedule?

side note

a. repayment amount R31 036

Expert Solution

Number of repaymentd = years*payment per year = (2033-2018)*2 = 30

	Semi Annual rate(M)=	yearly rate/12=	12.00%	Semi Annual payment=	31035.91
Half year	Beginning balance (A)	Semi Annual payment	Interest = M*A	Principal paid	Ending balance
1	250000.00	31035.91	30000.00	1035.91	248964.09
2	248964.09	31035.91	29875.69	1160.22	247803.86
3	247803.86	31035.91	29736.46	1299.45	246504.41
4	246504.41	31035.91	29580.53	1455.39	245049.03
5	245049.03	31035.91	29405.88	1630.03	243418.99
6	243418.99	31035.91	29210.28	1825.64	241593.36
7	241593.36	31035.91	28991.20	2044.71	239548.65
8	239548.65	31035.91	28745.84	2290.08	237258.57
9	237258.57	31035.91	28471.03	2564.89	234693.69
10	234693.69	31035.91	28163.24	2872.67	231821.01
11	231821.01	31035.91	27818.52	3217.39	228603.62
12	228603.62	31035.91	27432.43	3603.48	225000.14
13	225000.14	31035.91	27000.02	4035.90	220964.24
14	220964.24	31035.91	26515.71	4520.21	216444.04
15	216444.04	31035.91	25973.28	5062.63	211381.41
16	211381.41	31035.91	25365.77	5670.15	205711.26
17	205711.26	31035.91	24685.35	6350.56	199360.70
18	199360.70	31035.91	23923.28	7112.63	192248.07
19	192248.07	31035.91	23069.77	7966.15	184281.92
20	184281.92	31035.91	22113.83	8922.08	175359.84
21	175359.84	31035.91	21043.18	9992.73	165367.10
22	165367.10	31035.91	19844.05	11191.86	154175.24
23	154175.24	31035.91	18501.03	12534.89	141640.36
24	141640.36	31035.91	16996.84	14039.07	127601.29
25	127601.29	31035.91	15312.15	15723.76	111877.53
26	111877.53	31035.91	13425.30	17610.61	94266.91
27	94266.91	31035.91	11312.03	19723.88	74543.03
28	74543.03	31035.91	8945.16	22090.75	52452.28
29	52452.28	31035.91	6294.27	24741.64	27710.64
30	27710.64	31035.91	3325.28	27710.64	0.00

Where

Interest paid = Beginning balance * Semi Annual interest rate

Principal = Semi Annual payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Half year ending balance

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