Monthly compounding question with balance

Question

Suzanne opens a line of credit at a local bank, and immediately borrows 1870 dollars. 6 months later, she repays 1060 dollars. 5 months after the repayment, she borrows 570 more dollars. 6 months later, she repays 660 dollars. If no other transactions take place and the interest rate is 1 percent per month (compounded monthly), how much will she owe two years after she opened the line of credit?

 

I keep getting 744.1 dollars, which is not right answer

Answer 1

This type of value is often referred to as time value of money as it deals with the value of money at varying points of time.  As such, it is often easiest to solve these problems in a time line fashion.  To do that, first right down all transactions as they occur in time

(time is in months)

time 0: borrows $1870 at 1% interest compounded monthly

time 6: pay $1060

time 11: borrow $570

time 17: pay $660

 

so now solve it forward in time using the interest rate

 

at time zero she owes $1870.

 

Move forward 6 months, she now owes 1870*1.01^6=$1985.04

this is calculated using p*(1+i)^t, where p is the starting value, i is the interest rate per period of time and t is the number of periods of time.  Now she makes a payment of $1060 which brings her down to owing $925.04

 

Move forward another 5 months and she owes 925.04*1.01^5=2086.30, she borrows another 570 and thus now owes $2656.30

 

Move forward another 6 and she owes 2656.3*1.01^6=$2214.65 and she pays $660 bringing that down to $1554.65 owed.

 

Finally, we move forward another 7 months to get to 2 year (24 months) making the amount owed 1554.65*1.01^7=$2374.40

 

Thus the final answer is $2374.40