Question

Mr. Green borrows 100.000 $ at 10% compounded annually, agreeing to repay the loan in 20...

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?

Homework Answers

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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