Answer:
Edith would save more by paying off her loan 6 years early
Step-by-step explanation:
DORA
INTEREST: Â IF DORA PAID OFF THE LOAN IN 8 YEARS
       A  = (P(1 + r/m)^nm) - P
Where: Â A Â = The future amount
       P  = The principal sum  =  $83,000
       r   = The interest rate   = 10.7%
      n   = the time period    = 8
      m  = Number of times interest is paid in a year = 12
       A  = (P(1 + r/m)^nm) - P
         = ($83,000(1+10.7%/12)^8(12)) - $83,000
         = $83,000(1+ 0.107/12)^96 - $83,000
         = $83,000(2.3445) - $83,000
         = $194,593.50 - $83,000
         = $111,593.5
This means the interest if Dora paid the loan in 8 years is $111,593.50
INTEREST: Â IF DORA PAID OFF THE LOAN 6 YEARS EARLIER
A Â = (P(1 + r/m)^nm) - P
         = ($83,000(1+10.7%/12)^6(12)) - $83,000
         = $83,000(1+ 0.107/12)^72 - $83,000
         = $83,000(1.8949) - $83,000
         = $157,276 - $83,000
         = $74,276.70
This means the interest if Dora paid the loan in 6 years is $74,276.70
Savings if Dora paid the loan 6 years earlier = $111,593.5 - $74,276.70 = $37,316.80
EDITH
INTEREST: Â IF EDITH PAID OFF THE LOAN 8 YEARS EARLIER
A Â = (P(1 + r/m)^nm) - P
          A  = (P(1 + r/m)^nm) - P
         = ($93,000(1+10.7%/12)^8(12)) - $93,000
         = $93,000(1+ 0.107/12)^96 - $93,000
         = $93,000(2.3445) - $93,000
         = $218,038.50 - $93,000
         = $125,038.50
This means the interest if Edith paid the loan in 8 years is $125,038.50
INTEREST: Â IF EDITH PAID OFF THE LOAN 6 YEARS EARLIER
       A  = (P(1 + r/m)^nm) - P
         = ($93,000(1+10.7%/12)^6(12)) - $93,000
         = $93,000(1+ 0.107/12)^72 - $93,000
         = $93,000(1.8949) - $93,000
         = $176,255.70 - $93,000
         = $83,255.70
This means the interest if Dora paid the loan in 6 years is  = $83,255.70
Savings if Dora paid the loan 6 years earlier = $125,038.50 - $83,255.70 = $41,812.80
It is clear that Edith would save more by paying off her loan 6 years earlier since Dora savings is $37,316.80 and Edith savings is $41,812.80 if they paid the loan 6 years earlier
Answer:
Edith would save more because she borrowed $10,000 more in principal.
Step-by-step explanation:
