PLEASE HELP ??? :))
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The easiest way to do this is to use an iterative process.

P[n]=P[n-1](1+r)-m

where P is the current balance on the loan so that P[0]=$1100, n=month number starting at zero, m=monthly payment, r=monthly rate.

So m=$71.50, r=19.2/12%=1.6%=0.016.

Therefore P[n]=1.016P[n-1]-71.50.

The table below shows the decreasing balance:

n Balance ($)
0 1100.00
1 1046.10
2 991.34
3 935.70
4 879.17
5 821.74
6 763.38
7 704.10
8 643.86
9 582.67
10 520.49
11 457.32
12 393.13
13 327.92
14 261.67
15 194.36
16 125.97
17 56.48

At month 17 the balance is less than the monthly payment, so there are 18 payments in all, but the last payment is reduced to $56.48.

Algebraically the balance is P[n]=P(1+r)ⁿ-m((1+r)ⁿ-1)/r where P= initial loan.

From this, n=log(m/(m-rP))/log(1+r). Plugging in the values we get n=17.8 months. The table seems to confirm this if P[n]=0. If R=1+r, PRⁿ=m(Rⁿ-1)/r; rPRⁿ/m=Rⁿ-1; Rⁿ(1-rP/m)=1; Rⁿ=m/(m-rP).

by Top Rated User (906k points)

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