Question

Suppose that you have just borrowed $250,000 in the form of a 30 year mortgage. The loan has an annual interest rate of 9% with monthly payments and monthly compounding.

*** I NEED TO KNOW HOW TO SOLVE THIS ON A CALCULATOR. i AM USING A HP-10B2+

a. What will your monthly payment be for this loan?

b. What will the balance on this loan be at the end of the 12th year?

c. How much interest will you pay in the 7th year of this loan?

d. How much of the 248th payment will consist of principal?

Answer 1

To calculate this question we will take all the value on a monthly basis. So for a 30 year loan the total no of months will be 360. The monthly interest rate will be 9/12 = 0.75%

First we will calculate the monthly EMI with the help of calculator. I am also working on excel to give you the figures. On calculator its easy if the numbers are inserted correctly.

To calculate the EMI which is PMT on calculator: The letters in the bracket denotes the number we need to insert for that command. First type the number then press the key. For eg: 250,000 then press PV

Particulars	Amount
Present Value of the Loan - PV	250000
No of Months - N	360
Interest Year - I/Y	0.75%
Future Value - FV	0
EMI - PMT	-2,011.56

a) The EMI is 2011.56 we will get the number as negative but we need to consider the value and not the sign.

b) To calculate the value of the loan at the end of 12 year. First we need to calculate the no of months pending for the 30 year loan. At the end of 12 years we will have 216 months pending as 144 months will be over.

To calculate the future value of the loan we will use the following values

Particulars	Amount
Present Value of the Loan - PV	250000
No of Months - N	144
Interest Year - I/Y	0.75%
EMI - PMT	-2,011.56
Future Value - FV	-214806.9

We will get the value as 214806.9 this will be the loan amount left at the end of 12 year.

c) This will be calculated using the excel

7 years will have months from 73 to 84, Please find below the table.

Month	Principal	Interest Rate	Interest Amount	EMI	Balance principal
73	237025.8403	0.0075	1777.69	2011.56	236791.97
74	236791.9741	0.0075	1775.94	2011.56	236556.35
75	236556.3539	0.0075	1774.17	2011.56	236318.97
76	236318.9666	0.0075	1772.39	2011.56	236079.80
77	236079.7988	0.0075	1770.60	2011.56	235838.84
78	235838.8373	0.0075	1768.79	2011.56	235596.07
79	235596.0686	0.0075	1766.97	2011.56	235351.48
80	235351.4791	0.0075	1765.14	2011.56	235105.06
81	235105.0552	0.0075	1763.29	2011.56	234856.78
82	234856.7831	0.0075	1761.43	2011.56	234606.65
83	234606.649	0.0075	1759.55	2011.56	234354.64
84	234354.6389	0.0075	1757.66	2011.56	234100.74
Total			21213.62

In this we will first calculate the outstanding principal at the end of 72 months and then will calculate on monthly basis the interest amount. The total amount of interest paid in the year 7 will be 21213.62

d) First we will calculate the balance amount at the end of 247th loan which will be

Particulars	Amount
Present Value of the Loan - PV	250000
No of Months - N	247
Interest Year - I/Y	0.75%
EMI - PMT	₹ -2,011.56
Future Value - FV	₹ -1,52,918.23

Then we will calculate the 0.75% on the outstanding loan will be as follows:

Month	Principal	Interest Rate	Interest Amount	EMI	Balance principal
248	152918.23	0.0075	1146.89	2011.56	152053.55

The interest amount will be 1146.89 and the principal amount will be 864.67 (2011.56 - 1146.89)