Dora took out an 8-year loan for $83,000 at an APR of 10.7%, compounded monthly, while Edith took out an 8-year loan for $93,000 at an APR of 10.7%, compounded monthly. Who would save more by paying off her loan 6 years early?

Answer:Edith would save more by paying off her loan 6 years earlyStep-by-step explanation:DORAINTEREST:  IF DORA PAID OFF THE LOAN IN 8 YEARS              A  = (P(1 + r/m)^nm) - PWhere:  A  = 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                   = $111,593.5This means the interest if Dora paid the loan in 8 years is $111,593.50INTEREST:  IF DORA PAID OFF THE LOAN 6 YEARS EARLIERA  = (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                   = $74,276.70This means the interest if Dora paid the loan in 6 years is $74,276.70Savings if Dora paid the loan 6 years earlier = $111,593.5 - $74,276.70 = $37,316.80EDITHINTEREST:  IF EDITH PAID OFF THE LOAN 8 YEARS EARLIERA  = (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                   = $125,038.50This means the interest if Edith paid the loan in 8 years is $125,038.50INTEREST:  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                   = $83,255.70This means the interest if Dora paid the loan in 6 years is   = $83,255.70Savings if Dora paid the loan 6 years earlier = $125,038.50 - $83,255.70 = $41,812.80It 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