Question 1035865
Susan borrowed $5000. The terms of the loan were equal monthly payments at Susan 12% compounded monthly for 3 ysears. After making payments for 1 year,Susan decided to pay off the balance of the loan. A) what was susans monthly payment.B) how much must Susan pay at the end of 1 year to pay off the balance of the loan.C)How much interest did Susan save by repaying the loan in 1 year.
<pre>Monthly payment made = {{{highlight_green("$"166.07)}}}, using the payment formula, based on the present value of an ordinary annuity. 
This is: {{{PMT = PV[oa]/((1 - 1/(1 + i/m)^(mt))/(i/m))}}}, where:
PMT =    Monthly payment (unknown in this case)
{{{PV[oa]}}} = Present Value of an Ordinary Annuity ($5,000, in this case)
i =      Annual Interest Rate (12%, or .12, in this case)
m =      Compounding periods, per year (Monthly, or 12, in this case)
t =      Time, in years (3, in this case)

Calculating the amortization on this loan results in a total payment, in 1 year, of $1,992.86, of which $520.78 was applied to interest, and $1,472.08 applied to principal. 
The payoff amount, after 1 year then, was: $5,000 - $1,472.08, or {{{highlight_green(matrix(1,1, "$3,527.92"))}}}

If she'd continued to pay $166.07 over the 3-year period, she would've paid a total of $5,978.58, of which $978.58 would've been applied to interest.

By the time the loan was paid off (1 year's time), she'd paid $520.78 in interest. If she'd continued for the 3 years, she would've had to pay $978.58 in interest. 
Therefore, she saved: $978.58 - 520.78, or {{{highlight_green("$"457.80)}}}, in interest.