Question

Mr. Green borrows 100.000 $ at 10% compounded annually, agreeing to repay the loan in 20 equal annual payments. How much of the original principal is still unpaid after he has made the tenth payment?

Answer #1

Loan amount=PV=$100,000

Rate of interest =i=10%

Loan term=n=20 years

Annual payment, A, is given by

**A=PV*(A/P,0.10,20)=100000*(A/P,0.10,20)**

Let us calculate the interest factor

Plug in the value of interest factor in above relation.

**A=100000*0.11745962=$11745.96**

**Unpaid principal after 10th payment is given
as**

B10=100000*(F/P,0.10,10)-11745.96*(F/A,0.10,10)

Let us calculate the interest factors

(F/P,0.10,10)=(1+0.10)^10=2.59374246

So,

**B10=100000*2.59374246-11745.96*15.93742460=$72173.89**

**Unpaid principal after 10th
payment=$72,173.89**

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