Answer:
Edith would save more by paying off her loan 6 years early
Step-by-step explanation:
DORA
INTEREST: IF DORA PAID OFF THE LOAN IN 8 YEARS
A = (P(1 + r/m)^nm) - P
Where: 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
= $111,593.5
This means the interest if Dora paid the loan in 8 years is $111,593.50
INTEREST: IF DORA PAID OFF THE LOAN 6 YEARS EARLIER
A = (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: IF EDITH PAID OFF THE LOAN 8 YEARS EARLIER
A = (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: 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
