Find the balance due in 1 year to repay the loan.

Question

~~A loan of $1,000 is due in 1 year with simple interest at 14 ½% per annum. The debtor pays $200 in 3 months and $400 in 7 months. Find the balance due in 1 year to repay the loan.

Answer 1

We can also apply the Merchant’s Rule:

$1000(1+0.145)=$1145

Answer 2

$1000 is not due for another 12 months.

From this we need to subtract the effects of the early payments. The $200 payment is 9 months in advance and the $400 payment is 5 months in advance, so we need to deduct 200(1+0.145*3/4)+400(1+0.145*5/12) = $221.75+$424.17 = $645.92 from $1000=$354.08, which is the amount to be paid on the due date.

I treated this problem as a separate investment at 14½% of $200 for 9 months and of $400 for 5 months, the proceeds of which would contribute to pay off the debt of $1000 when it’s due. The proceeds total $645.92 so $354.08 is all that’s needed to make up the $1000 to cancel the debt.