Business Mathematics- Amortization of Loans, Including Residential Mortgages

Ivanthedumbfck

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i need some help with this question:

Pelican Recreational Services owe $27,500 secured by a collateral mortgage. The mortgage is amortized over 15 years by equal payments made at the end of every 3 months and is renewable after 3 years.

If the mortgage is renewed for a further 4 years but amortized over 8 years and interest is 7.5% compounded semi-annually, what is the size of the quarterly payments for the renewal period?

Here's what i did:

N=4x4=16
I=0.075/2=0.0375

C=2/4=1/2

P=(1+0.0375)^1/2-1=0.018577439

PV= PMT[1-(1+P)^-n]/P
27500= PMT[1-(1+0.018577439)^-16]/0.018577439
27500=PMT(13.73196962)
PMT=$2002.63

The correct answer is $1000.87




1
 
Hello Denis, sry about replying so late. It's been a busy 2 weeks. I forgot to add some questions to the problem which made it kinda vague. Here's the correct solutions to the question:

Pelican Recreational Services owe $27,500 secured by a collateral mortgage. The mortgage is amortized over 15 years by equal payments made at the end of every 3 months and is renewable after 3 years.

a.) If interest is 7% compounded annually, what is the size of the payments?
b.) How much of the principal is repaid by the fourth payment?
c.) What is the balance at the end of the 3-year term?
d.) If the mortgage is renewed for a further 4 years but amortized over 8 years and interest is 7.5% compounded semi-annually, what is the size of the quarterly payments for the renewal period?


a.) I=0.07
n=15x4=60
p=(1.07)^1/4-1= 0.017058525 27500=PMT[1-(1+P)^-60]/P PMT=735.80

b.) FV(Original Debt)=27500(1+P)^(4-1)= 28931.47
FV(Payment Made)= 735.80[(1+P)^3-1]/P= 2245.27
Balance= 28931.47-2245.27= 26686.2
Interest= 26686.2 x P= 455.23
Loan Repaid= 738.50-455.23=280.57

c.)
Balance= 23981.71

d.) PV= 23981.71 n=8X4=32 I=0.075/2= 0.0375 C=2/4=1/2 P=(1.0375)^(1/2)-1= 0.018577439

23981.71= PMT[1-(1+P)^-32]/P
PMT= 1000.87
 
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Hello Denis, sry about replying so late. It's been a busy 2 weeks. I forgot to add some questions to the problem which made it kinda vague. Here's the correct solutions to the question:

Pelican Recreational Services owe $27,500 secured by a collateral mortgage. The mortgage is amortized over 15 years by equal payments made at the end of every 3 months and is renewable after 3 years.

a.) If interest is 7% compounded annually, what is the size of the payments?
b.) How much of the principal is repaid by the fourth payment?
c.) What is the balance at the end of the 3-year term?
d.) If the mortgage is renewed for a further 4 years but amortized over 8 years and interest is 7.5% compounded semi-annually, what is the size of the quarterly payments for the renewal period?


a.) I=0.07
n=15x4=60
p=(1.07)^1/4-1= 0.017058525 27500=PMT[1-(1+P)^-60]/P PMT=735.80

b.) FV(Original Debt)=27500(1+P)^(4-1)= 28931.47
FV(Payment Made)= 735.80[(1+P)^3-1]/P= 2245.27
Balance= 28931.47-2245.27= 26686.2
Interest= 26686.2 x P= 455.23
Loan Repaid= 738.50-455.23=280.57

c.)
Balance= 23981.71

d.) PV= 23981.71 n=8X4=32 I=0.075/2= 0.0375 C=2/4=1/2 P=(1.0375)^(1/2)-1= 0.018577439

23981.71= PMT[1-(1+P)^-32]/P
PMT= 1000.87
b.) You could also use 735.80(1+p)^(-(60-4+1))
d.) From your given solution, I'd say you need to rephrase question d.) to minimize any ambiguity. Use of fancy terms like "renewed" amounts to nothing more than applying a different nominal rate from the beginning of the 4th year to the end of the 11th year to find the new quarterly payments.
 
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