Question

Henry borrows $1075 at 10.5% simple interest. He makes a partial payment of $200 at the end of 12 month(s), and a partial payment of $400 at the end of 16 months. Determine the amount required to settle the debt at the end of 22 months using (a) Merchant's Rule and (b) U.S. Rule. (a) Merchant's Rule: $ (b) U.S. Rule: $

Answer 1

Given that,

Henry borrowed $1075 at 10.5% simple interest.

He makes partial payment of $200 at the end of 12 months and a partial payment of $400 at the end of 16 months

let amount required to pay at end of 22 month be A,

Interest in simple interest is calculated using formula

Interest = Principal*interest rate*time

a). Merchant rule:

interest of amount borrowed for 22 months = 1075*0.105*22/12 = $206.94

So, total amount at 22 months = $1075 + 206.94 = $1281.94

interest of amount paid at month 12 at the end of 22 months(interest for 10 months) = 200*0.105*10/12 = $17.5

similarly, interest of amount paid at month 16 at the end of 22 months(interest for 6 months) = 400*0.105*6/12 = $21

So, Accumulated value of partial payment = 200 + 17.5 + 400 + 21 = 638.5

So, amount remaining = total amount at 22 months - Accumulated value of partial payment = 1281.94 - 638.5 = $643.44

b). US rule:

Loan amount = $1075

1 payment of $200 is made at the end of 12 month

So, interest on loan amount for 12 months = 1075*0.105*12/12 = $112.88

So, adjusted remaining value of payment = Loan + interest - partial payment = 1075 + 112.88 - 200 = $987.88

2nd partial payment of $400 is made after 4 months

So, interest on adjust remaining value = 987.88*0.105*4/12 = $34.58

So, adjusted remaining value of payment = previous adjusted remaining value + interest - partial payment = 987.88 + 34.58 - 400 = $622.45

Last payment is made after 6 months

So, interest for 6 months = 622.45*0.105*6/12 = $32.68

So, final payment = 622.45 + 32.68 = $655.13