Calculating Loans Flashcards
What are points?
Points are fees charged by lenders to either lower an interest or to originate the loan. Each point charged is 1 percent of the loan amount. For example, a discount point is charged up front to lower a borrower’s interest rate which in some cases helps the borrower qualify for the loan. In addition, a lender could charge a loan origination fee (point) to originate the loan
A lender is charging 1% loan origination fee and 2 discount points to the borrower. The loan amount is $150,000. What overall percentage is the lender charging? What is the percentage in points?
Formula:
Loan origination fee: 1%
Discount points: 2%
Total: 3%
Loan amount: $150,000
Total Charged - $150,000 x .03 total = $4,500.00 total
Points: $150,000 x .02 points = $3,000.00 total points charged
A borrower pays $500 for a $10,000 loan. How many points are paid?
$500 ÷ 10,000 = .05 = 5 points
A borrower pays 5 points on a $10,000 loan. What is the fee paid?
$10,000 x .05 = $500
A borrower pays $500 as 5 points on a loan. What is the loan amount?
$500 ÷ .05 = $10,000
What is the Annual interest?
The Annual interest is the annual amount of money someone pays to borrow money. Annual interest is calculated yearly, not monthly.
See T-bar formula for Annual Interest:
What are Loan Payments?
Loan Payments are the monthly amount paid on the loan that usually includes a principal portion and an interest portion.
ONLY the principal portion of the payment is applied to the principal balance owed on the loan.
The interest portion is not applied to the principal balance and therefore DOES NOT AFFECT the principal balance owed.
So, if a homeowner has a monthly payment of $620 and $120 of that payment is applied to interest, only $500 is actually applied to (and therefore lowers) the unpaid balance. This type of loan is said to be an “amortizing loan” because the principal balance is reduced with each payment until the principal is paid off completely. We will cover how to calculate a schedule of amortization in the next three slides.
But if the loan is an interest-only loan with a portion or the entire balance owed to be paid at a time in the future, interest is the only amount applied as a payment - as shown here - and the balance is not reduced until some or all of the principal is applied:
A borrower has a $100,000 interest-only loan @ 6% interest. What are the annual and monthly interest payments?
Annual interest payment = $100,000 x .06 = $6,000
Monthly interest payment = $6,000 ÷ 12 = $500
A borrower has a $500 monthly payment on a 6% interest-only loan. What is the loan principal?
First, multiply $500 by 12 to get the annual amount of interest, $500 x 12 = $6,000 annual interest. Next, divide: $6,000 ÷ 0.06 = $100,000 loan principal.
A borrower has a $500 monthly payment on a $100,000 interest-only loan. What is the loan rate?
First, multiply $500 by 12 to get the annual amount of interest, $500 x 12 = $6,000 annual interest. Next, divide the annual interest amount by the loan, $6,000 ÷ 100,000 = 0.06, and the loan rate is 6%
What is A fully amortized loan?
A fully amortized loan is one where the payments remain the same over a period of time and the principal and interest within the payments are paid in different increments (principal increasing each payment and interest decreasing each payment) over the life of the loan. An interest-only loan pays down the interest owed, none of the principal.
Formulas:
Interest-only loan: Total interest = Loan amount x Rate x Term in years
Fully Amortized loan: Total interest = (Monthly PI payment x 12 x term) - Loan amount
A borrower obtains a 10-year interest only loan of $50,000 @ 6%. How much interest will he or she pay?
($50,000 x .06 x 10) = $30,000
A borrower obtains a 10-year amortized loan of $50,000 @ 6% with monthly payments of $555.10. How much interest will he or she pay?
($555.10 x 12 x 10) - $50,000 = $16,612
What is Amortization Calculation?
Amortization Calculation
With an amortization loan, the amount of principal paid each month can be calculated using 3 factors: Principal Balance, Interest Rate, and Monthly Payment.
Formulas:
A 4 step method is used to calculate Principal and interest paid per month. The steps are
Multiply x, Divide (÷), Subtract - , and Subtract -.
Step 1: Principal x Interest = Annual Interest
Step 2: Annual Interest (÷) 12 months = 1st month’s Interest;
Step 3: Monthly Payment - 1st (or any) month’s calculated Interest = Principal paid;
Step 4: Principal Balance - Principal Paid = New Principal Balance.
A borrower obtains a 30-year $100,000 amortized loan @ 7% with a $665.31 monthly payment. What is the principal paid in the second month?
Month 1:
$100,000 x .07 (÷) 12 = $583.33 1st month’s Interest; Payment $665.31 - $583.33 = $81.98 First Month’s Principal;
$100,000 - $81.98 = $99,918.02 New Principal Balance
Month 2:
$99,918.02 x .07 (÷) 12 = $582.86 Second Month’s Interest; Payment 665.31 - 582.86 = $82.45 Second Month’s principal.
(you can subtract the $82.45 from the principal balance of $99,918.02 to obtain the new principal balance and continue the steps to fully show principal and interest amounts for the length of the loan.
What is A loan constant?
A loan constant is a number expressed as a percentage or decimal that calculates a mortgage payment which would retire the loan in the expressed time allotted or term of the loan.
Formula
Monthly payments= Loan amount/ 1000 times Loan Constant
Loan amount = Monthly payments/Loan Constant times1000
Loan Constant = Monthly payments/Loan amount times1000
A borrower obtains a loan for $100,000 with a 6.3207 constant. What is the monthly payment?
Monthly payment = ($100,000 ÷ 1,000) x 6.3207 = $632.07
A borrower has a monthly payment of $632.07 on a loan with a monthly constant of 6.3207. What is the loan amount?
Loan amount = ($632.07 ÷ 6.3207) x 1000 = $100,000
A borrower obtains a loan for $100,000 with a monthly payment of $632.07. What is the loan constant?
Loan constant = ($632.07 ÷ $100,000) x 1,000 = 6.3207
A borrower pays $1,000 for a $50,000 loan. How many points are paid?
$1,000 ÷ 50,000 = .02 = 2 points
A borrower pays 2 points on a $40,000 loan. What is the fee paid?
$40,000 x .02 = $800
A borrower has a $500,000 interest only loan @ 5% interest. What are the annual and monthly payments?
Annual payment = $500,000 x .05 = $25,000
Monthly payment = $25,000 ÷ 12 = $2,083
The loan officer at FirstOne Bank tells Amanda she can afford a monthly payment of $1,300 on her new home loan. Assuming this is an interest-only loan, and the principal balance is $234,000, what interest rate is Amanda getting?
The equation for the interest rate is (annual payment / loan amount) = interest rate. Thus ($1,300 x 12) / $234,000 = 6.67%.
The Kruteks obtain a fixed-rate amortized 30-year loan for $280,000 @ 6.25% interest. If the monthly payments are $1,724, how much interest do the Kruteks pay in the second month of the loan?
The fixed payment is principal and interest. To calculate, find the first month’s interest, then subtract it from the payment to arrive at the principal payment. Subtract the principal payment to determine the principal balance to calculate the second interest payment. If you subtract the second month’s interest from the principal amount of $279,734.33, you would be able to calculate the 3rd month’s interest. See Below:
280,000 X .0625 = $17,500 ÷ 12 = $1,458.33
Payment $1,724 - $1,458.33 = $265.67 first month principal
$280,000 - $265.67 = $279,734.33 Principal Balance
$279,734.33 X .0625 = $17,483.3956 ÷ 12 = $1,456.95 second month
A borrower obtains a loan for $200,000 with a 4.3207 constant. What is the monthly payment?
Monthly payment = ($200,000 ÷ 1,000) x 4.3207 = $864.14
A borrower obtains a 5-year interest only loan of $20,000 @ 7%. How much interest will he or she pay?
($20,000 x .07 x 5) = $7,000
What are The Loan-to-Value ratio?
The Loan-to-Value ratio shows the relationship between the amount borrowed and the appraised value of the property. Formula LTV = loan/price(value) Loan = LTV ratio times price(value) price(value) = loan/LTV ratio
A borrower can get a $265,600 loan on a $332,000 home. What is her LTV ratio?
LTV Ratio = $265,600 ÷ 332,000 = 80%
A borrower can get an 80% loan on a $332,000 home. What is the loan amount?
Loan = $332,000 x .80 = $265,600
A borrower obtained an 80% loan for $265,600. What was the price of the home?
Price (value) = $265,600 ÷ .80 = $332,000
What are Financial qualifications?
Financial institutions have to qualify a borrower prior to issuing a loan. Income ratio and debt ratio are two methods of qualification.
Income ratio qualification
Formula:
Monthly Principal & Interest (PI) payment = Income ratio x Monthly gross income
A lender uses a 28% income ratio for the PI payment. A borrower grosses $30,000 per year. What monthly PI payment can the borrower afford?
Monthly PI payment = ($30,000 ÷ 12) x .28 = $700
How much can the borrower borrow if the loan constant is 6.3207? (See also- loan constants)
Loan amount = ($700 ÷ 6.3207) x 1,000 = $110,747.22
What is Debt Ratio Qualification?
Formula
Debt Ratio= housing expense + other debt/ monthly gross income
housing expense = (monthly gross income X debt ratio)- other debt payments
A lender uses a 36% debt ratio. A borrower earns $30,000 / year and has monthly non-housing debt payments of $500.
What housing payment can she afford?
Housing expense = ($30,000 ÷ 12 x .36) - 500 = ($900 - 500) = $400
A mortgage lender uses an income qualification ratio of 28% for the monthly Principal, Interest, Taxes, and Insurance (PITI) payment. The Poormons earn $82,000 per year. If taxes are estimated to be $6,000 and insurance $1,200, how much can the Poormons afford to pay per month for the loan?
First, the Poormons can afford a monthly Principal, Interest, Taxes and Insurance payment of ($82,000 / 12 months x .28) to derive a total PITI payment of $1,913. Now take out the monthly taxes and insurance to derive the Principal and Interest (PI) portion of their payment: ($1,913 – $600) = $1,313 per month.
A lender offers an investor a maximum 70% LTV loan on the appraised value of a property. If the investor pays $230,000 for the property, and this is 15% more than the appraised value, how much will the investor have to pay as a down payment?
First, the sale price is 115% of the appraised value, so the appraised value is $230,000 / 115%, or $200,000. The lender will lend $140,000 (70% of appraised value), so the investor will have to come up with $90,000 ($230,000 – $140,000)
Assume FHA qualifies borrowers based on a 41% debt ratio, meaning that the borrower’s total monthly debt including the loan, taxes, insurance and non-housing debt cannot exceed 41% of the borrower’s monthly income. If a borrower grosses $4,000 per month and pays $600 monthly for non-housing debt obligations, what monthly payment for housing expenses can this person afford based on this ratio?
The formula here is (housing debt + $600) / ($4,000 monthly income) = 41%. Solving for housing debt, we have (housing debt + $600) = (41% x $4,000). Thus (housing debt + $600) = $1,640. Subtracting out non-housing debt, we have (housing debt = $1640 – $600), or housing debt = $1,040.
How much is a discount point?
1% of the loan amount.
A loan applicant has an annual gross income of $76,000. How much will a lender allow the applicant to pay for monthly housing expense to qualify for a loan if the lender uses an income ratio of 30%?
$76,000 ÷ 12 = $6,333, $6,333 x 0.30 = $1,900
A borrower obtained an 70% loan for $600,000. What was the price of the home (to the nearest thousand)?
$600,000 / 0.70 = $857,142.86
Christy has monthly loan payments of $1,200. Her loan is for $210,000 @ 6.1% interest. How much of her first payment goes towards principal?
$210,000 x 0.061 = $12,810, $12,810 ÷ 12 = $1,067.5, $1,200 - $1,067.50 = $132.50
Laura obtains a new loan @ 67% of her home’s price of $300,000. The loan constant is 6.321. What is Laura’s monthly payment?
$300,000 ÷ 1000 = $300, $300 x 6.321 = $1,896, $1,896 x 0.67 = $1,270
The loan officer at 2nd National Bank tells Lana she can afford a monthly payment of $1,900 on her new home loan. Assuming this is an interest-only loan, and the principal balance is $410,000, what interest rate is Lana getting?
$1,900 x 12 = $22,800, $22,800 ÷ $410,000 = 0.0556
A lender uses a 39% debt ratio. A borrower earns $40,000 / year and has monthly non-housing debt payments of $700. What housing payment can she afford?
$40,000 ÷ 12 = $3,333, $3,333 x 0.39 = $1,300, $1,300 - $700 = $600
Jerry recently obtained an 75% loan on his $410,000 home, and he had to pay $5,600 for points. How many points did he pay?
.75% times 410,000 = 307500, 5,600/ 307,500= 1.8 points
If you owe $14,000 on a new loan and pay $880 of interest for the year, your interest rate is?
$880 ÷ $14,000 = 0.063
A borrower has a $770,000 interest-only loan @ 5.5% interest. What are the monthly interest payments?
$770,000 x 0.055 = $42,350, $42,350÷ 12 = $3,529
The Browns obtain a fixed-rate amortized 30-year loan for $310,000 @ 6% interest. If the monthly payments are $1,815, how much interest do the Browns pay in the first month of the loan?
$310,000 x 0.06 = $18,600, $18,600 ÷ 12 = $1,550
A lender determines that a homebuyer can afford to borrow $160,000 on a mortgage loan. The lender requires an 80% loan-to-value ratio. How much can the borrower pay for a property and still qualify for this loan amount?
$160,000 ÷ 0.80 = $200,000
Steve is buying Darryl’s house for $360,000. Steve’s loan amount is $275,000. He has agreed to pay 2 points at closing. How much will Steve pay for points?
$275,000 x 0.01 = $2,750, $2,750 x 2 = $5,500
A home buyer pays $1,800 / month for the interest-only loan on his new house. The loan’s interest rate is 6%. If he obtained a 80% loan, what was the purchase price?
$1,800 x 12 = $21,600, $21,600 ÷ 0.06 = $360,000, $360,000 ÷ 0.80 = $450,000
Jackie obtains a 60% LTV loan on her new $250,000 home with an annual interest rate of 5.5%. What is the first month’s interest payment?
$250,000 x 0.60 = $150,000 loan, $150,000 x 0.055 = $8,250, $8,250 ÷ 12 = $688
A loan applicant has an annual gross income of $42,000. How much will a lender allow the applicant to pay for monthly housing expense to qualify for a loan if the lender uses an income ratio of 32%?
$42,000 ÷ 12 = $3,500, $3,500 x 0.32 = $1,120
Ginnie has an interest-only home equity loan at an annual interest rate of 7%. If her monthly payment is $1,458, how much is the loan’s principal balance?
$1,458 x 12 = $17,496, $17,496 ÷ 0.07 = $250,000
