Loan Repayments (1 Viewer)

[littlemisstiny]

Hey guys, I'm having issues with loan repayments at the moment and it is driving me absolutely insane. so..i need your help! [:

• A woman proposes to buy a house, of which the cash price is $100,000 by 20 equal annual instalments, the first payment to be made 12 months after the sale. If interest is charged on the loan needed at 9% p.a. , find the amount of each monthly installment.

Answer: $10954.65

What confuses me is when it says "first payment to be made 12 months after sale". I just dont understand how to interpret that. explain please? =]

I appreciate any help!
Thanks! =)

 

[lyounamu]

Hey guys, I'm having issues with loan repayments at the moment and it is driving me absolutely insane. so..i need your help! [:

• A woman proposes to buy a house, of which the cash price is $100,000 by 20 equal annual instalments, the first payment to be made 12 months after the sale. If interest is charged on the loan needed at 9% p.a. , find the amount of each monthly installment.

Answer: $10954.65

What confuses me is when it says "first payment to be made 12 months after sale". I just dont understand how to interpret that. explain please? =]

I appreciate any help!
Thanks! =)

20 annual installments means that, it is basically 20 years.

So, 100000 x 1.09^20 - AI(1+1.09+...+1.09^19) = 0

AI(1+1.09+...+1.09^19) = 100000 x 1.09^20
AI = $10954.6475...

To find the monthly installment, divide 9% by 12 = 0.0075
Then times 20 years by 12months/year = 320 months

Use the same formula or working out: 100000 x 1.0075^320 - MI(1+1.0075+...+1.0075^319) = 0
MI(1+1.0075+...+1.0075^319) = 100000 X 1.0075^320
MI = $825.567498...

 

[littlemisstiny]

LOL. well theres the proof showing my tendency to try make things harder for myself. i feel like such an idiot
thanks for your help [: