A mortgage is taken out for $10000 & is repaid by yearly instal of $2000. interest is charged on the debt @10%

Question

if the first repayment is made one year after the mortage is taken out find the number of years it takes for the motgage to be repaid

Answer 1

Interest after the 1st yr = 10,000*10%=1000
Balance after 1st repayment=10000+1000-2000
=9000

Interest after the 2nd year=9000*10%=900
Balance after 2nd repayment=9000+900-2000
=7900

Interest after the 3rd year=7900*10%=790
Balance after 3rd repayment=7900+790-2000
=6690

Interest after the 4th year=6690*10%=669
Balance after 4th repayment=6690+669-2000
=5359

Interest after the 5th year=5359*10%=535.9
Balance after 5th repayment=5359+535.9-2000
=3894.9

Interest after the 6th year=3894.9*10%=389.49
Balance after 6th repayment=3894.9+389.49-2000
=2284.39

Interest after the 7th year=2284.39*10%=228.44
Balance after 7th repayment=2284.39+228.44-2000
=512.83

Interest after the 8th year= 512.83*10%=51.28
Borrower makes last payment= 564.11

Therefore mortgage is repaid after 8 years.

Answer 2

It takes 9 years, but in the final year the payment is only 564.11

1. 10000
2. 11000 - 2000 = 9000 (+10% APR)
3. 9900 - 2000 = 7900 (+10% APR)
4. 8690 - 2000 = 6690 (+10% APR)
5. 7359 - 2000 = 5359 (+10% APR)
6. 5894. 90 - 2000 = 3894.90 (+10% APR)
7. 4284.39 - 2000 = 2284.39 (+10% APR)
8. 2512.83 - 2000 = 512.83 (+10% APR)
9. Final payment = 564.11

I think this is correct

Answer 3

Wee Eck is absolutely correct
Note that 11000 is 10000+10%APR on 10000
simiarly 9900 = 9000+10%APR on 9000
and so on