Question

A $45,000 direct reduction loan is financed at 9.25% per annum. The monthly payment is $385. What is the total number of monthly payments to pay off the loan? What are the amounts paid toward interest and principal in the 14th period? What is the remaining principal balance after the 14th payment has been made?

Answer 1

1.

Total number of monthly payment 301.14 months (approximately):

Using financial calculator BA II Plus - Input details:	#
FV = Future Value =	$0.00
PV = Present Value =	$45,000.00
I/Y = Rate = 9.25/12 =	0.770833
PMT =	-$385.00
CPT > N = Total number of period in months =	301.14

.

2.

Interest and principal paid during 14^th payment. For this we should know outstanding balance at end of 13^th month:

Finding outstanding balance at end of the particular time
P = Principal Loan =	$45,000.00
R = Rate or APR =	9.25%
n = Total number of payments done =	13
PMT = Payment = P x R/12 x (1+R/12)^N / ((1+R/12)^N - 1)	$385.00
FV = Outstanding Balance = (P*(1+R)^n)-(PMT*((1+R)^n-1)/R)
FV = Outstanding Balance = (45000*(1+9.25%/12)^13)-(385*((1+9.25%/12)^13-1)/(9.25%/12) =	$ 44,480.79

Now, we can calculate the required:

Interest payment = Outstanding x Interest rate /12 = $44480.79 x 9.25%/12 = $342.87

Principal payment = PMT – Interest payment = 385 - 342.87 = $42.13

.

3.

Outstanding principal balance at 14^th period:

Finding outstanding balance at end of the particular time
P = Principal Loan =	$45,000.00
R = Rate or APR =	9.25%
n = Total number of payments done =	14
PMT = Payment = P x R/12 x (1+R/12)^N / ((1+R/12)^N - 1)	$385.00
FV = Outstanding Balance = (P*(1+R)^n)-(PMT*((1+R)^n-1)/R)
FV = Outstanding Balance = (45000*(1+9.25%/12)^14)-(385*((1+9.25%/12)^14-1)/(9.25%/12) =	$      44,438.66

.

Manual calculation table below:

Year	Opening balance of loan	Interest	Payment	Amortization of loan	Closing balance
Y	OP	I = OP x Rate/12	PMT	AM = PMT - I	CB
1	45,000.00	346.88	385.00	38.13	44,961.88
2	44,961.88	346.58	385.00	38.42	44,923.46
3	44,923.46	346.28	385.00	38.72	44,884.74
4	44,884.74	345.99	385.00	39.01	44,845.73
5	44,845.73	345.69	385.00	39.31	44,806.41
6	44,806.41	345.38	385.00	39.62	44,766.80
7	44,766.80	345.08	385.00	39.92	44,726.87
8	44,726.87	344.77	385.00	40.23	44,686.64
9	44,686.64	344.46	385.00	40.54	44,646.10
10	44,646.10	344.15	385.00	40.85	44,605.25
11	44,605.25	343.83	385.00	41.17	44,564.08
12	44,564.08	343.51	385.00	41.49	44,522.60
13	44,522.60	343.20	385.00	41.80	44,480.79
14	44,480.79	342.87	385.00	42.13	44,438.66