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