Question

A bank lends you $20,000 at an interest rate of 0.5% per month for 24 months. You repay the loan in equal payments of $P each month. Give the formulae for the following quantities (i) the loan balance Am+1 after m + 1 months in terms of the loan balance Am after m months and the data.

(ii) the monthly payment $P.

(iii) What is the maximum interest expense that you will pay in any month?

(iv) Do you expect the total interest payment on this loan to be more more than, equal to, or less than, $1,000? (Circle one).

(v) Do you expect the outstanding balance on the loan after 12 months to be more than, equal to, or less than, $10,500? (Circle one).

(vi) Suppose that you want to borrow $20,000 at this interest rate of 0.5% per month but want to have payments that are no more than $800 per month. What is the formula for the minimum number of payments that you will have to make?

(vii) Will it take you more than 30 months to pay off this loan if you pay $800 per month. Yes, No (Circle one).

Answer 1

1 Equal monthly payment= p*r*(1+r)^n/((1+r)^n-1)

p is the principal amount = 20000

r is the rate of interest =0.5% per month

n is the no of months = 24

so 20000*0.5%*(1+5%)^24/((*(1+5%)^24)-1)

= 100*(1.005)^24/((1.005)^24-1)

=886.41

so amortization schedule for 1 month

month	Equal monthly payment A	Loan amount B	Interest on loan B*0.5%=C	pricipal repayment = D=A-C	Loan balance (B-D)
1	886.41	20000	100=20000*0.5%	786.41	19213.59

i so loan balance after m+1 months= 19213.59$

II. monthly payment of P= 886.41$

III Maximum interest will be paid in the first installment because of the higher amount of loan outstanding so the maximum interest paid is interest paid in first month = 100$

IV total interest payment on this loan to be more be more than 1000$ and amortization schedule is as follows.which indicate total interest paid = 1274$

month	Equal monthly payment A	Loan amount B	Interest on loan B*0.5%=C	pricipal repayment = D=A-C	Loan balance (B-D)
1	886.41	20,000	=20000*0.5% = 100	786	19,214
2	886.41	19,214	96	790	18,423
3	886.41	18,423	92	794	17,629
4	886.41	17,629	88	798	16,831
5	886.41	16,831	84	802	16,028
6	886.41	16,028	80	806	15,222
7	886.41	15,222	76	810	14,412
8	886.41	14,412	72	814	13,598
9	886.41	13,598	68	818	12,779
10	886.41	12,779	64	823	11,957
11	886.41	11,957	60	827	11,130
12	886.41	11,130	56	831	10,299
13	886.41	10,299	51	835	9,464
14	886.41	9,464	47	839	8,625
15	886.41	8,625	43	843	7,782
16	886.41	7,782	39	848	6,934
17	886.41	6,934	35	852	6,083
18	886.41	6,083	30	856	5,227
19	886.41	5,227	26	860	4,366
20	886.41	4,366	22	865	3,502
21	886.41	3,502	18	869	2,633
22	886.41	2,633	13	873	1,760
23	886.41	1,760	9	878	882
24	886.41	882	4	882	0
		Total	1274$

v  I expect the outstanding balance on the loan after 12 months to be less than, $10,500 from the above table loan amount after 12 month is10299$

VI p*r*(1+r)^n/((1+r)^n-1) from this formula we need to find n

vII No it will not take more than 30 months to pay the loan because if w epay at 886 per month it is taking 24 months so we reduce it 10% i,e from 886 to 800 then the intallments will increase by approx 10% . it takes 26 to 27 months