Question

You take out a mortgage loan from First Bank of Terlingua with the following characteristics:

-compounding period is monthly

-loan is for $200,000

-APR = 3.91%

-initial maturity is 30 years

-this mortgage loan has no points

Now suppose that First Bank allows you to accelerate your loan payments by paying an additional $100 each month. (We assume that the bank does not charge a fee for exercising this option.) When we take the acceleration into account, what is your effective annual rate?

Do not round at intermediate steps in your calculation. Report the rate in percent to three decimal places. Do not type the % symbol.

Answer 1

We will use excel while solving this question as there will be 360 monthly payments (30 years x 12 months a year).

	A	B
1	Principal	200000
2	Term	30
3	Interest Rate per annum	3.91%
4	Payments per year	12
5	Interest Rate per month	0.3258%
6	Total Periods (Payment)	360
7	Per Month Payment	=PMT(B5,B6,B1)

In the above table, A & B are representing the column number and 1,2,3,4,5,6&7 are representing the row number.

So the Amount '200000' is in cell number 'B1'

So using the function =PMT(Interest rate, Number of payments, preent value)

we found the monthly payment amount i.e.,

	A	B
1	Principal	$200,000.00
2	Term	30
3	Interest Rate per annum	3.91%
4	Payments per year	12
5	Interest Rate per month	0.3258%
6	Total Periods (Payment)	360
7	Per Month Payment	($944.48)

Now

The Bank Allows to repay additional $100 each month to accelerate loan repayment without any charges.

So now we have to find effective interest rate for 30 years

MonthlyPayment will be $944.48(Calculated Above) + $100(Additional Payment) = $1044.48 per month

Now we have the data

	A	B
1	Principal	$200,000.00
2	Term	30
3	Payments per year	12
4	Total Periods (Payment)	360
5	Per Month Payment	-$1,044.48

We have to calculate effective interest rate

For this, we will use the formulae

	A	B
1	Principal	$200,000.00
2	Term	30
3	Payments per year	12
4	Total Periods (Payment)	360
5	Per Month Payment	-$1044.48
6	Interest Rate per month	=RATE(B4,B5,B1)

In the above table, A & B are representing the column number and 1,2,3,4,5,6 are representing the row number.

So the Amount '200000' is in cell number 'B1'

So using the function =RATE(Number of payment, per month payment, principal value of loan)

Now we have the solution

	A	B
1	Principal	$200,000.00
2	Term	30
3	Payments per year	12
4	Total Periods (Payment)	360
5	Per Month Payment	-$1,044.48
6	Interest Rate per month	0.397%
7	Interest Rate per annum	4.760

Effective annual rate is 4.760

I hope it will help you in the study.

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