Respuesta :
Answer:
actual monthly payment is $1755.14
reduction on total principal = $199,911.54
reduction in principal = $197,876.64
Explanation:
given data
time period = 30 year = 30 × 12 = 360 months
loan amount = $200,000
interest rate = 10% = \frac{0.10}{12} = 0.008333
solution
we apply here amount formula that is
amount = [tex]\frac{principal \times r }{(1-(1+r)^{-t}}[/tex] ................1
put here value
amount = [tex]\frac{200000 \times 0.008333 }{(1-(1+0.008333)^{-360}}[/tex]
solve it we get
amount = 1755.14
actual monthly payment is $1755.14
and
we get here reduction that is
reduction = total loan - monthly payment .............2
reduction = $200,000.00 - $1755.14
reduction = $198,244.86
so here interest will be
interest = principal × rate .....3
interest = $200,000 × 0.008333
interest = 1666.67
so principal paid amount is $1755.14 - $1666.67
principal paid amount = $88.47
so reduction on total principal will be
reduction on total principal = $200,000.00 - $88.46
reduction on total principal = $199,911.54
and
After two year amount paid is
amount paid = 24 month × 1755.14
amount paid = $42,123.36
and interest paid will be after 2 year
interest paid = 24 months × 1666.67
interest paid = $40,000
so principal amount will be
principal = $42,123.36 - $40,000
principal = $2123.56
so we get reduction in the principal that is
reduction in principal = $200,000.00 - $2123.56
reduction in principal = $197,876.64
