Amortizing loans Suppose that you take out a 30-year mortgage loan of $200,000 at an interest rate of 10%. a. b. c. A)What is your total monthly payment? B)How much of the first month’s payment goes to reduce the size of the loan? C)How much of the payment after two years goes to reduce the size of the loan?

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 =   ................1

put here value

amount =  

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

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