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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: 12Many on May 31, 2018, 09:48:10 pm

Title: Compound Interest Question
Post by: 12Many on May 31, 2018, 09:48:10 pm
Xavier Borrowed 245 000 to pay for a house.
For the first 10 years of the loan, the interest rate was 4.35% per annum, compounding monthly.
Xavier made monthly repayments of $1800.
After 10 years, the interest rate changed.
If Xavier now makes monthly repayments of $2000, he could repay the loan in a further five years.
The new annual interest rate is closest to ?   

(What is the formula to finding the new annual interest) Is it  I=PRT?
Title: Re: Compound Interest Question
Post by: S200 on May 31, 2018, 09:53:09 pm
Quote from: 12Many on May 31, 2018, 09:48:10 pm
What is the formula to finding the new annual interest?
 Is it  I=PRT?
Wouldn't you just continue using the compound interest formula?
Because it's only the rate that has changed, it says nothing about changing the compounding sequence...
Title: Re: Compound Interest Question
Post by: MAGGOT on May 31, 2018, 10:25:46 pm
You can just plug the numbers into financial solver and find the future value (FV) and then using the FV as the new PV (change the sign to positive) solve for the interest rate (I%) which I get 4.12% p.a.
Title: Re: Compound Interest Question
Post by: 12Many on May 31, 2018, 10:36:54 pm
Quote from: MAGGOT on May 31, 2018, 10:25:46 pm
You can just plug the numbers into financial solver and find the future value (FV) and then using the FV as the new PV (change the sign to positive) solve for the interest rate (I%) which I get 4.12% p.a.
.  Wouldn't it also be  1800(.0.0435)^12X5.   = Which equates to 4.13 ( Using the compound Interest formula)? 
Title: Re: Compound Interest Question
Post by: Lear on May 31, 2018, 10:41:11 pm
Just use financial solver honestly.
Part 1
N= 10x12
I = 4.35
PV = 245000
PMT = -1800
FV=?
CPY/PPY = 12

Find FV, turn it into positive
Part 2
N= 12x5
I=?
PV = FV found in part 1
PMT = -2000
FV = 0
CPY/PPY= 12

And solve for I (interest rate)
Title: Re: Compound Interest Question
Post by: plato on June 04, 2018, 11:46:28 pm
Quote from: 12Many on May 31, 2018, 10:36:54 pm
.  Wouldn't it also be  1800(.0.0435)^12X5.   = Which equates to 4.13 ( Using the compound Interest formula)? 
The compound interest formula cannot be used when there is a regular payment to reduce the balance. After each payment, the principal is reduced a little and the amount of interest to be paid at the next payment is reduced. Then, a larger portion of the next payment will reduce the principal even further.
The financial solver should be used for questions such as this.