Mortgages_ Annuities_ and Loans

Loans, Mortgages, and Annuities Allison Keith & Carly Mueller April 6, 2008 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. How do I calculate a loan? A Bn i the loan amount (principal) LOANS… the balance after n payments have been made the interest rate per period, not per year (For instance, if the loan payments are made monthly and the interest rate is 9%, then i = 9%/12 = 0.75% = 0.0075.) n P the number of time periods elapsed at any given point the amount of each equal payment (can be rearranged to solve for any variable) 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: A=50,000 n=24 i=.0056 P=575.40 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 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 you’ll repay the money you’ve borrowed to buy your home.” 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. • 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 won’t change for 10 years but after, will be adjusted. • 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 home’s 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 you’ll just pay the interest or work off some principal. 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. =.004167 =180 (5% interest rate compounded monthly) (number of payments = 12 months * 15 years) = ((1+i)^n) = 2.11383 = Because P=$100,000, then M = $790.81 The monthly payment would be: $790.91. In order to determine how much you are paying the bank over the course of the mortgage… = (M*n)-(loan amount) =(790.81*180)-$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. 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 . P=$200,000 i=0.005416666667 N=360 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 (M*n)-(loan amount) = ($1264.14*360)-$200,000 = $255,090 Over the course of 30 years, you will be paying back $255,090 to the bank on your loan. 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 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.” 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 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. 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 FV= =$6800.67 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-annuity-2.html BIBLIOGRAPHY… • • • • • • • • • • • • "Adjustable Rate Mortgages." The Federal Reserve Board. 10 Feb. 2009.. "Annuities Calculator." Cool Math.. "Annuities." US Securities and Exchange Commission. 17 Jul. 2005.. "Loan calculator and amortization." Bankrate.. "Loan." Investor Words.. "Which Mortgage is Right for You?." AOL Real Estate. 11 Nov. 2008.. Brown, Stan . "Loan or Investment Formulas." Oak Road Systems.. Pritchard, Justin . "Fixed Rate Mortgages." About.. Razzi, Elizabeth . "Mortgage Loan Types." Bankrate. 19 Mar. 2007.. "Radnor Twp Home Loans & Radnor Twp Rates." Yahoo Real Estate.. Russell, Deb . Understanding Annuities.. Weintraub, Elizabeth . "Mortgage Loan Types." About..