Loans, Mortgages, and Annuities

1
Loans, Mortgages, andAnnuities

• Allison Keith Carly Mueller
• April 6, 2008

2
LOANS
What is a loan?

• An arrangement in which a lender gives money or
  property to a borrower, and the borrower agrees
  to return the property or repay the money,
  usually along with interest, at some future
  point(s) in time. Usually, there is a
  predetermined time for repaying a loan, and
  generally the lender has to bear the risk that
  the borrower may not repay a loan
• Two things to keep in mind
• The original sum of money (the principal)
  increases as interest accumulates
• Payments can be made against the principal.

3
(No Transcript)
4
LOANS
How do I calculate a loan?
(can be rearranged to solve for any variable)
5
Example of a Student Loan
Suppose I have student loans totaling 50,000.
The interest rate on these loans is 6.8, and is
paid over 10 years. I have just made my 24th
payment of 575.40 and would like to know the
current balance
A50,000 i.0056 n24 P575.40
B
42,514.01
After paying 24 payments (2 years) of your 10
year mortgage, you have a balance of 42,514.01
to pay on your 50,000 student loan.
http//www.bankrate.com/brm/popcalc2.asp
6
MORTGAGES
What is a mortgage?

• A mortgage is a legal contract on a
  property/house that secures a loan is paid in
  installments over a set period of time. The
  mortgage secures your promise that youll repay
  the money youve borrowed to buy your home.

7
MORTGAGES
Types of Mortgages

• 30 year fixed rate mortgage
• Steady, predictable payments (interest rate and
  payment will remain fixed for 30 years)
• Helps to plan long-term finances because it is so
  predictable
• Interest rate is generally higher than most other
  loan types
• 15 year fixed rate mortgage
• Offers quicker repayment and faster equity build
  up than the 30 year mortgage.
• Interest expenses are much lower than the 30 year
  rate
• Example A fifteen year 300,000 mortgage would
  cause you to pay more than 700 more a month, but
  would save you over 200,000 in interest.
• 40 year or 50 year mortgages
• You receive lower monthly payments by stretching
  out the loan
• However, in the long run, this ends up costing
  you a lot of money.
• Example A fifty year 300,000 mortgage would
  save you over 200 a month and would cause you to
  pay over 300,000 more in interest.

8

• Adjustable-rate mortgage (ARM)
• It allows you to start off with low payments so
  you can afford more at the time.
• Interest rate will adjust every year, and are
  linked to an economic index.
• The lender will add a specific margin to the
  index.
• The index is a measure of interest rates
  generally, and the margin is an extra amount that
  the lender adds
• Borrowers are protected from very large interest
  rates by two caps. Typically, your rate can rise
  or fall by no more than 2 percentage points per
  year. Over a lifetime, it can rise by no more
  than 6 percentage points.
• Lenders generally charge lower initial interest
  rates for ARMs than fixed mortgages.
• Hybrid ARMs These will have a fixed interest
  rate for a certain period of time and then the
  rate adjusts for the remainder of the loan
• Examples include 10/1, 7/1 and 3/1. The first
  number is the length of the initial period. So
  on 10/1, this interest rate wont change for 10
  years but after, will be adjusted.

9

• Balloon/Reset Mortgages
• They have monthly mortgage payments based on a 30
  year schedule. However, the entire balance is
  due at the end of a 5 or 7 year term, unless you
  choose to reset your mortgage.
• This gives the person the advantage of having low
  monthly payments, but the loan must be paid, or
  reset, at the end of a specified term. This
  means that you can reset your mortgage interest
  rate at the market rate for the remainder of the
  30-year period.
• Subprime Mortgages
• Normally made for borrowers with low credit
  ratings.
• Lending institutions often charge interest on
  these mortgages that is greater than conventional
  mortgages in order to compensate for the risk
  that is associated.
• Interest Only Mortgage
• Allows buyers to pay just the interest on a
  mortgage for a fixed term.
• After this, payments will rise.
• This is for people who believe that their homes
  value will rise or who expect to earn a higher
  salary within the next few years.
• Option Mortgage
• This is designed for people who do not have a
  steady income
• Monthly payments are extremely low
• You decide each month whether youll just pay the
  interest or work off some principal.

10
MORTGAGES
How do I determine my monthly payment on an Fixed
Rate Mortgage? (compounded monthly)
Suppose I have a 100,000 mortgage at a 5
interest rate (compounded monthly) for 15 years.
(5 interest rate compounded monthly)
.004167
180
(number of payments 12 months 15 years)
((1i)n) 2.11383

Because P100,000, then M 790.81
The monthly payment would be 790.91.
11

• In order to determine how much you are paying the
  bank over the course of the mortgage
• (Mn)-(loan amount)
• (790.81180)-100,000
• 142,525.80 - 100,000
• 42,525.80
• Over the course of the 100,000 mortgage over 15
  years, you will be paying 42,525.80 to the bank.
  

12
MORTGAGES
How do I determine my monthly payment on an Fixed
Rate Mortgage?
Suppose I have a 200,000 mortgage with a fixed
yearly nominal interest rate of 6.5 for 30 years
.
P200,000 i0.005416666667 N360
Equation to determine the Monthly Payment on FRM
After plugging these numbers into the formula,
our monthly payment on this fixed rate mortgage
would be 1264.14
(Mn)-(loan amount) (1264.14360)-200,000
255,090
Over the course of 30 years, you will be paying
back 255,090 to the bank on your loan.
13
The cost of borrowing to buy a home is now at its
lowest level in almost 4 decades According to
Freddie Mac, the average 30-year fixed rate
mortgage is at 4.78 percent during the week of
March 29th, 1 percent lower than it was a year
ago.
Yahoo! Real Estate
14
(No Transcript)
15
ANNUITIES
What is an annuity?

• According to the SEC, an annuity is a contract
  between you and an insurance company, under which
  you make a lump-sum payment or series of
  payments. In return, the insurer agrees to make
  periodic payments to you beginning immediately or
  at some future date.

16
ANNUITIES

• There are two types of annuities Fixed and
  Variable
• Fixed
• Guaranteed that your account will earn a minimum
  rate of interest
• Periodic payments are a guaranteed amount per
  dollar in your account
• These payments may last for a definite period of
  time (20 years) or an indefinite period of time
  (your lifespan)
• Variable
• You choose to invest your purchase payments in
  various investment options (usually mutual funds)
• Your rate of return and the amount of purchase
  payments you receive varies depending on the
  performance of your investment options

17
ANNUITIES
What is the Annuity formula?

• You can use this formula to solve for the future
  amount of money you will have after a certain
  amount of payments have been made, or to
  determine the number of payments required to
  obtain a desired future sum of money.

18
ANNUITIES
How do I determine my future value?

• Example
• What is the value of a monthly contribution of
  100 over 5 years at an interest rate of 5?
  compounding monthly.
• For this example,
• n 5yrs 12 months 60
• i .05/12 .004167
• The future value with this monthly contribution
  is 6800.67
• The reverse is also true, if you have a lump sum
  of money, you can convert it to an annuity
  payout. So the lump sum of money (the portion
  that is left after each payment) earns interest
  and then is periodically paid out. This can be
  used to create an income in retirement.
• Example A person has accumulated 400,000 and
  would like to know how much that would pay him
  each month for the next 30 years. Interest rates
  are 5.

http//www.coolmath.com/calculators/calculator-ann
uity-2.html
19
BIBLIOGRAPHY

• "Adjustable Rate Mortgages." The Federal Reserve
  Board. 10 Feb. 2009.lthttp//www.federalreserve.gov
  /pubs/arms/arms_engligt.
• "Annuities Calculator." Cool Math.lthttp//www.cool
  math.com/calculators/calculator-anngt.
• "Annuities." US Securities and Exchange
  Commission. 17 Jul. 2005.lthttp//www.sec.gov/answe
  rs/annuity.htmgt.
• "Loan calculator and amortization."
  Bankrate.lthttp//www.bankrate.com/brm/popcalc2.asp
  gt.
• "Loan." Investor Words.lthttp//www.investorwords.c
  om/2858/loan.htmlgt.
• "Which Mortgage is Right for You?." AOL Real
  Estate. 11 Nov. 2008.lthttp//realestate.aol.com/ar
  ticle/finance/_a/whichgt.
• Brown, Stan . "Loan or Investment Formulas." Oak
  Road Systems.lthttp//oakroadsystems.com/math/loan.
  htmgt.
• Pritchard, Justin . "Fixed Rate Mortgages."
  About.lthttp//banking.about.com/od/mortgages/a/fix
  edmortggt.
• Razzi, Elizabeth . "Mortgage Loan Types."
  Bankrate. 19 Mar. 2007.lthttp//www.bankrate.com/br
  m/news/Financial_Literacgt.
• "Radnor Twp Home Loans Radnor Twp Rates." Yahoo
  Real Estate.lthttp//realestate.yahoo.com/Pennsylva
  nia/Radnor_Twp/loans?p19085redir1gt.
• Russell, Deb . Understanding Annuities.lthttp//mat
  h.about.com/od/businessmath/ss/annuitiesgt.
• Weintraub, Elizabeth . "Mortgage Loan Types."
  About.lthttp//homebuying.about.com/od/financingadv
  ice/qt/gt.