Question

On 2001/6/1, Peter borrowed $6000, agreeing to pay interest at 1.7%/year compounded monthly. He paid $1200 on 2005/2/1, and $1500 on 2007/8/1. What equal payments on 2011/6/01, and 2013/12/01 will be needed to settle the debt?

Remark: Dates are given in the format YYYY/MM/DD

Answer 1

Amount borrowed on June 1, 2001 = $6000 @ 1.7% interest p.a. compounded monthly

1st payment of $1200 was made on Feb 1, 2005 i.e. after 44 month after the loan was taken

2nd payment of $1500 was made on Aug 1, 2008 i.e. after 86 month after the loan was taken

Let's first calculated the present value of above repayment to find the remaining loan amount

PV = FV/(1+i/n)^nt

PV of 1st payment = 1200/(1+.017/12)^44 = $1127.53

PV of 2nd payment = 1500/(1+.017/12)^86 = $1328.06

Total remaining amount = 6000 - 1127.53 - 1328.06 = $3544.41

Let peter made 3rd payment of X on June 1, 2011 i.e. after 120 month of the loan and 4th payment of X on Dec 1, 2013 i.e. after 150 month of the loan

So PV of both the payment must be equal to $3544.41

So, 3544.41 = X/(1+.017/12)^120 + X/(1+.017/12)^150

=> X = $2145

So peter need to make equal payment of $2145 on  2011/6/01, and 2013/12/01 to settle the debt.