D. Use this equation to calculate your mortgage payment: PMT PVI/ (-(i)-n) 1. Ca

Question

D. Use this equation to calculate your mortgage payment: PMT PVI/ (-(i)-n) 1. Calculate your monthly mortgage payment at the 680-699 above rate for 15 years. 4.03%. arr 4.03. /. 2. Calculate your monthly mortgage payment at the 680-699 rate for 30 years. E. Calculate your total payments and interest. Multiply your monthly mortgage payment by the number of months for your time period. Then subtract the loan principal amount. 1. 15 years Total payments: Total interest 2. 30 years Total payments: Total interest:

Explanation / Answer

D)

1)

We are given the following values

PV

$201,650

I

4.03/12 = 0.3358%

n

15 x 12 = 180

Using the given formula

PMT = (PV x I)/((1 - (1 + I)^(-n)))

On substituting the values, we get

PMT1 = $1494.614062 or $1494.61

2)

Here, n = 30 x 12 = 360

Using the same formula, we get

PMT2 = $966.20

E)

Total Payments = PMT x n

Interest Paid = Total Payments - Principal

So, in case 1 and 2

Total Payments

Principal

Interest

1

$269,030.53

$201,650

$67,381

2

$347,831.57

$201,650

$146,182

F)

The following is the amortization schedule generated at the website http://www.bankrate.com/calculators/mortgages/amortization-calculator.aspx

The values to be entered are mortgage $201,650, term in years 30 and interest rate 4.03%. Click on calculate and then Show amortization schedule to get the required answer.

1)

For 30 years

Monthly payments is $966.20

DATE

PAYMENT

PRINCIPAL

INTEREST

TOTAL INTEREST

BALANCE

Dec. 2017

$966.20

$288.99

$677.21

$677.21

$201,361.01

Jan. 2018

$966.20

$289.96

$676.24

$1,353.45

$201,071.05

Feb. 2018

$966.20

$290.94

$675.26

$2,028.71

$200,780.11

Mathematical Explanation

For Month 1

Our opening balance is the loan amount outstanding= $201,650

We begin by calculating the interest = $201650 x 0.3358% = $677.21

This amount out of PMT of $966.20 goes towards the interest payment.

The remaining amount = $966.20 - $677.21 = $288.99, goes towards reducing out outstanding balance.

So, balance amount at the end of month 1 = 1 $201,650 - $288.99 = $201,361.01.

For Month 2

Our opening balance is the loan amount outstanding at the beginning of month 2 = amount outstanding at the end of month 1 = $201,361.01

So, the interest = $201,361.01 x 0.3358% = $676.24

This amount out of PMT of $966.20 goes towards the interest payment.

The remaining amount = $966.20 - $676.24 = $289.96 , goes towards reducing out outstanding balance.

So, balance amount at the end of month 1 = $201,361.01 - $289.96 = $201,071.05.

The total interest paid up to the end of month 2 is therefore = $677.21 + $676.24 = $1,353.45

2)

Payment #120 is

Payment #

PAYMENT

PRINCIPAL

INTEREST

TOTAL INTEREST

BALANCE

120

$966.20

$430.68

$535.52

$73,322.62

$159,028.77

So, Total interest paid = $73,322.62

And Total amount paid towards principal = Original principal - Balance = $201,650 - $159,028.77 = $42,621.23

3)

We have to look for the date when value in column 3 becomes greater than value in column 4. This is

Oct. 2030

$966.20

$484.30

$481.90

$91,118.88

$143,008.06

This is the 155th payment

4)

The difference = $146,181.57 - $67,380.53 = $78,801.04

You refer to E above or go through the last row of the amortization schedules.

5)

Being a rational human being we would always prefer to pay less. So, lesser the loan amount the better.

However, we will have to look at what monthly PMT we can afford. If I am able to pay comfortably $1495 in a month I will be better off going for higher monthly payment and smaller duration. However, if my monthly income permits me to spare less then that I would go for the other option of 30 years and $966.2.

Obviously it is always better to pay for the house with as much cash as you possible can if the interest rate that you pay on the loan is greater than the interest rate offered on safe investments (like a bond, T-bill) in the market.

However, we also have to look at the benefit that one gets to one's income tax payments. Interest payment on a mortgage are tax deductible and offer the benefit of reducing the taxable income up to the actual interest or the permissible limit by the tax authorities, whichever is lower.

G)

1)

PITI is acronym the sum of monthly principal, interest, taxes, and insurance.

2)

For the 30 years loan, we will have to calculate the 4 components separately.

We will have assume the values of taxes and insurance. For ease of understanding

Let, Annual property tax be = $1200

Annual home insurance cost = $1200

So the monthly costs become

Monthly taxes = $1200/12 = $100

Monthly insurance = $1200/12 = $100

So,

PITI = principal + interest + taxes+ insurance = $966.20 + $100 + $100 = $1,166.2

Given,

PITI = 0.28 x Monthly income

So,

Monthly Income = PITI/ 0.28 = $1,166.2/0.28 = $4,165

PS- You can use additional information if it is given in the question.

3)

Other costs may be arrangement fee (for the product), booking fee, valuation fee for determining the actual worth of the property, missed payments fee, broker fee, closing costs, early repayment charge.

Closing costs is the fees charged for closing the mortgage loan.

When we close a loan, the fees that we pay to the lender at closing in exchange for a reduction in the interest rate.

We are allowed to answer only 4 subparts to a question so you will ahve to reask the queston for answer to part H.

PV

$201,650

I

4.03/12 = 0.3358%

n

15 x 12 = 180

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.