Amortizing loans Suppose that you take out a 30-year mortgage loan of $200,000 at an interest rate of 10%. 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?

Explanation:

The first step is to calculate an APR payment amount. This is done by adding your closing costs to your loan amount, and then calculating a new monthly payment at your loan's interest rate. In this case, if you borrowed $200,000.00 + at 10% for 30 years,

A=(P×i)/(1-(1+i)^-n)

Where,

P= principal amount = $200,000.00

n=number of month = 12×30 years= 360 months

i= monthly interest rate= 10%= 0.1/12=0.008333

Therefore,

A=(P×i)/(1-(1+i)^-n)

A=($200,000×0.008333)/(1-(1+0.008333)^-360)

A=(1666.667)/(1-(1.008333)^-360)

A=(1666.667)/(1-0.05041)

A=1666.667/0.9496

A=$1755.14

The actual monthly payment is $1755.14

b. How much of the first month’s payment goes to reduce the size of the loan.

The first month payment is $1755.14

The total loan is $200,000.00

Then the reduction is

$200,000.00 - $1755.14

It has reduce the loan to $198,244.86

The interest on the payment is P×i=$200,000×0.008333=1666.67

Then, the principal paid is 1755.14-1666.67=$88.47

Then the reduction on the total principal is $200,000.00 - $88.46=

$199,911.54

c. How much of the payment after two years goes to reduce the size of the loan?

Let know how much he has paid after 2years, which is 24months

After 2years he will have paid

24×1755.14=$42,123.36.

Interest paid too will be

24×1666.67=$40,000

Then, the principal paid will be

$42,123.36 - $40,000=$2123.56

Then the reduction in the principal is $200,000.00 - $2123.56= $197,876.64

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