Question

Henry borrows $850 at 14.5% simple interest. He makes a partial payment of $170 at the end of 10 month(s), and a partial payment of $340 at the end of 14 months. Determine the amount required to settle the debt at the end of 20 months using (a) Merchant's Rule and (b) U.S. Rule.

Answer 1

US RULE

Henry Borrowed = 850$

Simple Interest = 14.5% per anum

First Payment that he made at the end of 10 Months, so he will pay simple interest on 850$ for 10 months

= 850*14.5%*10/12

=102.7083$

Till Second Payment he would have outstanding Balance of 850-170 = 680

Second Payment is done at the end of 14 months, Interest on 680 would be for 4(14-10) Months = 680*14.5%*4/12 = 32.8667$

Till Next Payment he would have outstanding Balance of 680-340 = 340

To settle debt is done at the end of 20 months, Interest on 340 would be for 6(20-14) Months = 340*14.5%*6/12 = 24.65$

Amount that he has to pay at the end of 20th month would be = Interest Accrued till now + Outstanding Balance at the end of 20th month

=102.7083 + 32.8667 + 24.65 + 340

= 500.225$

Merchants Rule

Months	Beginning Balance (A)	Interest (B)	Payments ©	Ending Balance (A+B-C)
10 Months	850	102.70833	170	782.7083333
14 Months	782.7083333	37.830903	340	480.5392361
20 Months	480.5392361	34.839095		515.3783307

Interest = Beginning Balance *Interest rate*Number of months interest accrued/Number of months in an year

First Interest Months = 10

Second Interest Months (14-10) = 4

Third Interest Months (20-14) = 6