Question

A loan of ​$13 comma 000 with interest at 12​% compounded semi dash annually is repaid by payments of $ 937.00 made at the end of every three months. ​(a) How many payments will be required to amortize the​ loan? ​(b) If the loan is repaid in full in 2 years​, what is the payout​ figure? ​(c) If paid​ out, what is the total cost of the​ loan? ​(a) The number of payments required to amortize the loan is nothing. ​(Round up to the nearest whole​ number.)

Answer 1

Solution to (a)
Number of repayments (upto 3rd quarter of 5th year) = 19 (see the schedule below)
Loan Amortisation Schedule
Year	Months	Opening Balance	Repayment (6 months) [937x2]	Interest Portion (6 months) [ iii x 6% ]	Principal Portion [ iv - v ]	Closing Balance [ iii - vi ]
(i)	(ii)	(iii)	(iv)	(v)	(vi)	(vii)
1st year	0-6	13,000	1,874	780	1,094	11,906
6-12	11,906	1,874	714	1,160	10,746
2nd year	0-6	10,746	1,874	645	1,229	9,517
6-12	9,517	1,874	571	1,303	8,214
3rd year	0-6	8,214	1,874	493	1,381	6,833
6-12	6,833	1,874	410	1,464	5,369
4th year	0-6	5,369	1,874	322	1,552	3,817
6-12	3,817	1,874	229	1,645	2,172
5th year	0-6	2,172	1,874	130	1,744	429
6-9*	429	442	13*	429	-
Notes
1) Loan Amortisation Schedule is prepared for each half year (as interest is compounded semi-annually) and hence 2 quarterly repayments are clubbed.
2) In the 5th year, repayment is complete during the third quarter (i.e during 6-9 months as seen in the schedule)* and hence interest for the same ($13) is calculated at 3%

Solution to (b)
Repayment amount is $ 16,412 (see the schedule)
Year	Months	Loan Amount (Opening)	Interest for half year (6%)	Total Amount (Closing)
1st year	0-6	13,000	780	13,780
6-12	13,780	827	14,607
2nd year	0-6	14,607	876	15,483
6-12	15,483	929	16,412

Solution to [c)

Total Cost of the loan is the interest paid which is $ 3,412

[ Interest = Repayment Amount - Loan Borrowed = 16,412-13,000 ]