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MarvellousFeynman

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San José City College

Amber Hatter

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loan types financial mathematics mortgages finance

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This document provides an overview of major loan types, including fixed-rate and adjustable-rate mortgages. It explores calculations and examples related to simple and compound interest formulas used in loan analysis. It also discusses various loan structures, amortization, and relevant financial concepts.

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6. Major Loan Types By Amber Hatter Overview Before establishing the Federal Housing Administration (FHA) mortgage insurance program in 1938, the mortgage landscape lacked fixed-rate, regularly amortizing options. The introduction of amortization, where payments cover both interest and principal, re...

6. Major Loan Types By Amber Hatter Overview Before establishing the Federal Housing Administration (FHA) mortgage insurance program in 1938, the mortgage landscape lacked fixed-rate, regularly amortizing options. The introduction of amortization, where payments cover both interest and principal, revolutionized loan repayment. Initially, loans were primarily interest-only, often short-term, with potential call provisions. The FHA and subsequent VA Loan Guarantee Programs ushered in long-term fixed-rate, regularly amortized loans, aligning with market conditions post-World War II. This shift emphasized the importance of tailored loan programs to meet borrowers' needs amidst fluctuating interest rates. Today, the mortgage market offers various repayment plans, reflecting current market dynamics and enabling loan officers to match borrowers with suitable options effectively. Agenda Six ways to calculate a loan Fixed Rate Mortgages Adjustable-rate mortgages (nontraditional loan types) I. Six Ways to Calculate a Loan 1. 2. 3. 4. 5. 6. Simple Interest Formula (I = P X R X T) Compound Interest Formula [A = P (1 + r/n)^nt] Mortgage Payment Tables (Time Value of Money) Financial Calculator (i.e. HP10BII, etc.) Excel Spreadsheet Online Calculators 1. Simple Interest Formula (I = P x R x T) For straight notes (non-amortized loans) Simple Interest (I) = Principal (P) x Rate (R) x Time (T) Maturity value (MV) = Principle (P) + Interest (I) Banker’s rule (360 days) Interest (I) – the cost of using someone else’s money (or the amount you receive for lending your money. Principal (P) – the amount of money borrowed Rate of Interest (R) – the annual percent that must be paid to use the money. Time (T) – the term of duration a borrower has use of money expressed in years (or part of a year). 1. Simple Interest Formula, an Example Solve I Solve P Solve R Solve T Solve MV Solve Date What is the interest on $10,000 @ 8% per year for one year? I=PxRxT I = 10,000 x.08 x 1 I = $800 What is the principal amount borrowed if a 9% rate of interest results in payment of $135 interest for a period of 6 months? P = I ÷ (R x T) P = $135 ÷ (.09 x 6/12) P = $135 ÷ (.09 x.5) P = $135 ÷ (.045) P = $3,000 On a $3,000 loan for 6 months, $146.25 was paid as interest. What was the rate of interest? R = I ÷ (P x T) R = $146.25 ÷ ($3,000 x.5) R = $146.25 ÷ $1,500 R =.0975 or 9.75% How long did a borrower have use of $42,000 if a 9 ½% rate of interest cost her $9,975? T = I ÷ (P x R) T = $9,975 ÷ ($42,000 x.095) T = $9,975 ÷ $3,990 T = 2.5 years, or 2 ½ years, or 2 years and 6 months You borrow $30,000 for office furniture. Your loan is for 6 months at an annual interest rate of 8%. What is the maturity value? I = $30,000 x.08 x 6/12 = $1,200 MV = $30,000 + $1,200 = $31,200 On June 15, you borrow $9,000 for whatever. Your loan is for 60 days at an annual interest rate of 11%. What is the due date? The due date is 8/14: June 15-30=15 days July 31 = 31 days 46 – 60 = 14 *This is for a straight note (non-amortized) 2. Compound Interest Formula [A = P (1 + r/n)^nt] A = the future value of the investment loan, including interest P= principal investment amount (the initial loan amount) r = the annual interest rate (decimal) n = the number of times that interest is compounded per unit t = the time the money is invested or borrowed for 2. A fully amortized 1-year loan, an example: Inputs Loan Amount $12,000 Annual Interest Rate 6.000% Term of Loan 1 Year First Payment Date 1/1/20 Frequency of Payment Monthly Summary Rate (per period) 0.500% Payment (per period) $1,032.80 Total Payments $12,393.58 Total Interest $393.58 2. How do I use the formula? Month 1: Loan balance ($12,000 x 6%) / 12 months = $60 interest portion House payment (P&I) $1,032.80 - interest $60 = Principal $972.80 Loan balance $12,000 – principal $972.80 = new balance 11,027.20 2. How do I amortize the first 3-months? Month 2: Loan balance ($11,027.20 x 6%) / 12 months $55.14 interest portion House payment (P&I) $1,032.80 - interest $55.14 = Principal $977.66 Loan balance $11,027.20 – principal $977.66 = new balance 10,049.54 Month 3: Loan balance ($10,049.54 x 6%) / 12 months $50.25 interest portion House payment (P&I) $1,032.80 - interest $50.25 = Principal $982.55 Loan balance $10,049.54 – principal $982.55 = new balance $9,066.99 What happens after the last payment is made? No. 1 2 3 4 5 6 7 8 9 10 11 12 Due Date 1/1/2020 2/1/2020 3/1/2020 4/1/2020 5/1/2020 6/1/2020 7/1/2020 8/1/2020 9/1/2020 10/1/2020 11/1/2020 12/1/2020 Payment Due 1,032.80 1,032.80 1,032.80 1,032.80 1,032.80 1,032.80 1,032.80 1,032.80 1,032.80 1,032.80 1,032.80 1,032.78 Additional Payment 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Interest 60.00 55.14 50.25 45.33 40.40 35.44 30.45 25.44 20.40 15.34 10.25 5.14 Principal Balance 972.80 977.66 982.55 987.47 992.40 997.36 1,002.35 1,007.36 1,012.40 1,017.46 1,022.55 1,027.64 $12,000.00 11,027.20 10,049.54 9,066.99 8,079.52 7,087.12 6,089.76 5,087.41 4,080.05 3,067.65 2,050.19 1,027.64 0.00 3. Payment Tables Payments per thousand dollars financed. Find the interest rate, move across to the Term column, and multiply that number by the number of dollars financed. Ex.#1: 4.375 percent, 40-year Term on $100,000 loan. Thus, $4.42 x 100 (thousands) = $442.00 Principal and interest payment Ex. #2: 6.500 percent, 30-year Term on $150,000 loan. Thus, $6.32 x 150 (thousands) = $948.00 principal and interest payment. 4. Financial Calculators HP10BII Loan Payments On a $100,000 loan at 10 percent for 30 years, what is the monthly (P&I) payment? 100,000 [PV] 10 [I/YR] 360 [N] [PMT] -877.57 5. Excel Spreadsheets I. Fixed-Rate Mortgages >Explained As of April 9, 2024: 10-year fixed: 6.27% [Bankrate] 15-year fixed: 6.09% [NerdWallet] 20-year fixed: 6.71% [NerdWallet] 30-year fixed: 6.83% [NerdWallet] i. Definition A fixed-rate mortgage is a type of mortgage loan where the interest rate remains constant throughout the entire term of the loan, regardless of changes in the market interest rates. This means that the borrower's monthly mortgage payments, which include both interest and principal components, remain unchanged from the first payment to the last. ii. What are the pros & cons of FRMs? Pros Cons Predictability in payments with a fixed interest rate throughout the life of the loan, facilitating easier budgeting and financial planning. Higher initial interest rates and monthly payments compared to the initial rates of adjustable-rate mortgages (ARMs). Less flexibility compared to ARMs, as refinancing is required to take advantage of falling interest rates. Potentially higher overall interest cost if interest rates decrease and the borrower does not refinance. Longer terms (e.g., 30 years) result in paying more interest over the life of the loan compared to shorter-term loans. Qualifying for a fixed-rate mortgage might be more challenging during periods of high-interest rates, as the initial payments are higher than those of some adjustable-rate options. Immunity to rising interest rates in the market, ensuring your mortgage payments do not increase over time. Simplicity and ease of understanding for borrowers, making it a straightforward mortgage option. Long-term cost savings if interest rates rise significantly after securing a low fixed rate. Variety of term lengths available, allowing borrowers to choose a payment schedule that fits their financial goals. iii. What are the types of Fixed-Rate Mortgages? Type Example Traditional FRM’s: 30-Year: Offers lower monthly payments over a long term. 15-Year: Higher monthly payments but significant interest savings over a shorter term. 20-Year: A middle ground between 30-year and 15-year terms. Balloon Mortgage: A balloon mortgage is a fixed-rate loan with reduced initial monthly payments, culminating in a significant final payment at the loan's end. This payment structure, exemplified by a 360/180 scenario, entails partial amortization. Biweekly Mortgages: Payments are made every two weeks, reducing interest and loan term. Short-Term FRMs: 10-Year: Rapid equity build-up with high monthly payments. Long-Term FRMs: 40-Year: Lowest monthly payments but higher total interest cost. Jumbo Mortgages: For loan amounts exceeding conforming loan limits, with fixed rates. Government-Backed FRMs: FHA Loans: Lower down payment requirements, insured by the Federal Housing Administration. VA Loans: For eligible veterans, often with no down payment. USDA Loans: For rural homebuyers, potentially offering 100% financing. II. AdjustableRate Mortgages > Explained www.google.com (4/10) 10 / 6 ARM 7.867% 7 / 6 ARM 8.016% 5 / 6 ARM 7.918% 3 / 6 ARM 7.875% i. Definition An Adjustable-Rate Mortgage (ARM) is a type of mortgage with an interest rate that adjusts periodically according to a specific financial index, affecting both the interest rate and monthly payments within established limits. Unlike fixed-rate mortgages, which have a uniform rate throughout the loan term (e.g., 15 or 30 years), ARMs undergo rate modifications at predetermined intervals, guided by a particular index and a fixed margin, leading to potential rate and payment fluctuations. ii. What are the pros and cons of ARM’s? Pros Cons Lower initial interest rates and monthly payments compared to fixed-rate mortgages, making them more affordable in the short term. Interest rates and monthly payments can increase over time, potentially becoming unaffordable. Potential for interest rates and payments to decrease if market rates fall. Interest rate caps provide some protection against dramatic increases in interest rates and payments. Ideal for borrowers who plan to move, refinance, or expect a future income increase before the rate adjusts. The initial fixed-rate period offers temporary stability in interest rates and payments. The complexity and variability of terms can be difficult for some borrowers to understand. Risk of negative amortization if the payment adjustments do not keep pace with the interest rate changes. Uncertainty in future payment amounts makes long-term budgeting and financial planning challenging. Potential need to refinance if rates increase significantly, which could incur additional costs and is subject to market conditions. iii. What are some common adjustable-rate mortgages? Hybrid ARMs A Hybrid ARM This loan is a hybrid of a fixed-rate period and an adjustable-rate period The interest rate is fixed for a short-term period, then the rate may adjust annually A 3/1 ARM will have a 3-year fixed-rate period, after that may adjust annually for the remaining term A 3/1, 5/1, 7/1, 10/1 The first number indicates how long the fixed interest rate will be; and The second number indicates how often the rate will adjust after the initial period Common Indexes of ARMs Index Name Description Moving Treasury Average (MTA) Average yield of U.S. Treasury securities adjusted to a 1-year maturity, calculated over the past 12 months. Prime Lending Rate Interest rate charged by banks to their most creditworthy customers for short-term loans. Treasury Constant Maturity Average interest rate on all outstanding U.S. Treasury securities with a remaining term equal to the index's Indices (TCM) or (CMT) maturity (e.g., 1-year CMT reflects average rate for 1-year Treasuries). 11th District Cost of Funds (COFI) Cost incurred by banks in the 11th Federal Home Loan Bank District to attract deposits. Monthly Median Cost of Funds National average interest rate paid by savings institutions to attract deposits. Certificate of Deposits Index Average yield on 3-month certificates of deposit (CDs) over the past year. LIBOR Index (London Interbank Offered Rates) Average interest rate that major banks charge each other for short-term loans in the London Interbank Market. Consumer Price Index (CPI) Not commonly used, but possible future ARM index that reflects inflation. ARM Components Feature Description Index Changes in the interest rate are governed by a financial index. The lender chooses an index for each ARM product that is out of their influence. Margin This is a predetermined amount that is added to the index to determine the fully indexed interest rate. Margins are generally set for the term of the loan. Fully Indexed Accrual Rate (FIAR) This is the index plus the margin. This is how we calculate the rate at the time of the adjustment. Discount/Short Fall A one-time reduction to make the initial rate competitive. The result is also called the “teaser rate.” This is the Start Rate. The amount of the discount is decided by the investor. Initial Rate/Start Rate Teaser Rate Wat the lender charges for the first period of the ARM. It is the FIAR minus the discount. Periodic Adjustment Cap This limits the amount the interest rate can adjust up or down from one adjustment to the next after the first adjustment. Also known as the subsequent adjustment cap. Usually 1% or 2%. Initial Adjustment Cap This limits the amount the interest rate can adjust up or down after the first adjustment. Usually, it is 5% or 6%. Not all loans have a different initial adjustment cap than the periodic adjustment cap. Lifetime Cap Limits the amount of upward interest rate over the full term of the loan. Usually, it is 5% or 6%. Negative Amortization This occurs when the interest on a loan is accruing at a faster rate than it is being repaid. ARM Caps Adjustable-rate mortgages (ARMs) typically include several kinds of caps that control how your interest rate can adjust. An ARM may have different cap structures. A 10/1 ARM has a 10-year fixed-rate period, after that may adjust annually for the remaining term and different lenders may offer different Cap Options. As an example, a 10/1 Arm may offer: 2/6 Caps The first number indicates the initial interest rate cap The second number indicates the subsequent adjustment cap annually 5/2/6 Caps The first number indicates the initial interest rate cap The second number indicates the subsequent adjustment rate cap annually The third number indicates the lifetime adjustment rate cap Example Of A 10/1 ARM With 2/6 Caps Index 1 Year MTA : Discount: Margin: 1.375% 1.00% 2.75% Annual Adjustment Cap: Lifetime Adjustment Cap *11th year Index: A. Calculate the Fully Indexed Rate: Index +Margin 1.375 2.75 Fully Indexed Rate 4.125% B. Calculate the Starter/Teaser Rate: Index +Margin 1.375 2.75 -Discount 1.00% Starter/Teaser Rate 3.125% C. Calculate Maximum 11th Year Rate: Starter Rate +Annual Adj. Cap 3.125% 2.00% Max 1st Year Rate 5.125% (New Current*) Index 2.25%* +Margin 2.75% *New FIAR 5.00% D. Calculate 11th Year FIAR: *New FIAR is the maximum new adjusted Rate if lower than the Max adjusted capped Rate calculation 2.00% 6.00% 2.25% Example Of A 10/1 ARM With 2/6 Caps Index 1 Year MTA : Discount: Margin: 1.375% 1.00% 2.75% Annual Adjustment Cap: Lifetime Adjustment Cap *11th year Index: 2.00% 6.00% 2.25% C. Calculate Maximum 11th Year Rate: Starter Rate +Annual Adj. Cap 3.125% 2.00% Max 1st Year Rate 5.125% (New Current*) Index 2.25%* +Margin 2.75% *New FIAR 5.00% D. Calculate 11th Year FIAR: If the Index on year 11 is 2.25 (as used in the example above) What is the Interest Rate that would be charged to the customer? *New FIAR is the maximum new adjusted Rate if lower than the Max adjusted capped Rate calculation ** The FIAR is typically rounded to the nearest 1/8 if being using as the interest rate Example Of A 10/1 ARM With 5/2/6 Caps Index: Discount:.750% 1.00% Margin: 2.750% A. Calculate the Fully Indexed Rate: Index +Margin Fully Indexed Rate Annual Adjustment Cap: Initial Adjustment Cap: Lifetime Adjustment Cap: 11th year Index: 1.375 2.75 4.125% B. Calculate the Starter/Teaser Rate: Index 1.375 +Margin -Discount 2.75 1.00% Starter/Teaser Rate 3.125% C. Calculate Maximum 11th Year Rate: Starter Rate +Annual Adj. Cap 3.125% 5.00% Max 1st Year Rate 8.125% (New Current*) Index 2.25%* +Margin 2.75% *New FIAR 5.00% D. Calculate 11th Year FIAR: *New FIAR is the maximum new adjusted Rate if lower than the Max adjusted capped Rate calculation 2.000% 5.000% 6.000% 2.25% Example Of A 10/1 ARM With 5/2/6 Caps Index: Discount:.750% 1.00% Margin: 2.750% C. Calculate Maximum 11th Year Rate: Starter Rate Annual Adjustment Cap: Initial Adjustment Cap: Lifetime Adjustment Cap: 11th year Index: 2.000% 5.000% 6.000% 2.25% 3.125% +Annual Adj. Cap 5.00% Max 1st Year Rate 8.125% (New Current*) Index 2.25%* +Margin 2.75% *New FIAR 5.00% D. Calculate 11th Year FIAR: If the Index in year 11 is 2.25 (as used in the example above) What is the Interest Rate that would be charged to the customer? *New FIAR is the maximum new adjusted Rate if lower than the Max adjusted capped Rate calculation ** The FIAR is typically rounded to the nearest 1/8 if being using as the interest rate The End

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