Question

A loan officer states, "Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage." Calculate the difference in payments on a 30-year mortgage at an interest rate of 1% a month versus a 15-year mortgage with an interest rate of 1.2% a month. Both mortgages are for $100,000 and have monthly payments. What is the difference in total dollars that will be paid to the lender under each loan? (Round the monthly payment amounts to 2 decimal places.) If you use the financial calculator, tell me your inputs and output (i.e. pv,fv,n, i/Y, pmt).

please write the steps and solve step by step

Answer 1

1.Information provided:

Present value= $100,000

Time= 30 years*12= 360 months

Interest rate= 1%/12= 0.0833% per month

The monthly payment is calculated by entering the below in a financial calculator:

PV= -100,000

N= 360

I/Y= 0.0833

Press the CPT key and PMT to compute the amount of monthly payment.

The value obtained is 321.64.

Therefore, the amount of monthly payment is $321.64.

2.Information provided:

Present value= $100,000

Time= 15 years*12= 180 months

Interest rate= 1.2%/12= 0.10% per month

The monthly payment is calculated by entering the below in a financial calculator:

PV= -100,000

N= 180

I/Y= 0.10

Press the CPT key and PMT to compute the amount of monthly payment.

The value obtained is 607.33.

Therefore, the amount of monthly payment is $607.33.

Difference in total payments:

= ($321.64*360) - ($607.33*180)

= $115,790.40 - $109,319.71

= $6,470.69.

In case of any query, kindly comment on the solution.