Question

A debt of $1200 is to be paid off by payments of $500 in 45 days, $300 in 100 days, and a final payment of $ 436.92. Interest is at r = 11%. and merchant rule was used to calculate the final payment. In how many days should the final payment be made?

Answer 1

let x be the days after debt final payment is made

debt value = 1200

interest accumulated = 1200 * 0.11 * x/365

1st payment = 500

interest accumulated = 500 * 0.11 * (x-45)/365

2nd payment = 300

interest acccumulated = 300 * 0.11 * (x-100)/365

3rd payment = 436.92

=>

1200 (1+ 0.11 * x/365 ) = 500 * (1+ 0.11 * (x-45)/365 ) + 300 * (1+ 0.11 * (x-100)/365 ) + 436.92

=>

1200 + 0.36164383561x = 500 + 0.1506849315x - 6.78082191781 + 300 + 0.0904109589x - 9.04109589041 + 436.92

=>

0.12054794521x = 21.0980821918

=>

x = 175.01

= 175 days

hence final payment made in 175 days