paying back loans (part 2) - inetteacher.com...paying back loans (part 2) regular/multiple loan...
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However, in the majority of loans, the lender wants scheduled payments, not just one lump sum. This is common for mortgages and vehicle loans.
There are three common types of regular payment schedules: . Monthly· Biweekly· Semi Monthly· Accelerated Biweekly
Paying Back Loans (Part 2)Regular/Multiple Loan Payments
To see the differences between these, we will consider a loan payment of $600 per month. The amount paid each year will vary depending on which type of payment plan you choose.
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Ex. For a loan that has a $600 per month payment, determine how much will be paid out at the end of 3 years, using each of the 4 payment options.
Monthly:
Biweekly: 1. Find biweekly payment first.(every 2 weeks)(26 times a year)
2. Find the amount paid out in 3 years
SemiMonthly: 1. Find semimonthly payment.(twice a month)(24 times a year)
2. Find the amount paid out in 3 years.
Accelerated Biweekly: 1. Find accelerated biweekly payment first.(monthly payment )2)26 times a year
2. Find amount paid out in 3 years.
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Ex: 130 biweekly payments are required to pay off a loan. How many years does this represent?
Ex: 288 semi monthly payments are required to pay off a loan. How many years does this represent?
Ex: 390 accelerated biweekly payments are required to pay off a loan. How many years does this represent?
When people purchase a vehicle, they often link their loan payment schedule to their payroll schedule. Why is this the case?
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The formulas that we learned previously (i.e A = P (1 + rt) and A = P(1 + i)n) ONLY apply to single loan payments at the end of a term, and thus CANNOT be used in situations in which there is a regular loan payment. What we will do for these types of questions is refer to a table (can be manually created or using software) which shows the payment, interest principal and balance.
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Ex: Mark is buying an ATV for the summer. The bank offers him a loan of $7499.99 to pay for his ATV with an interest rate of 4.5% compounding monthly. If Mark makes 36 monthly payments of $223.10, calculate the total interest paid at the end of the loan.
(A) Complete the first three rows of the Amortization table...
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1. Interest Paid = (interest rate per year )# compounding periods) H Outstanding Balance 2. Principal Paid = Monthly Payment – Interest
3. Current Balance = Previous Balance Principal – Paid during Current Payment Period
The entire table (as created using software) is shown below:
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Determining the Cost of a Loan Using Technology
To calculate a loan payment requires a more complicated formula. Usually, we use a TVM Solver (TVM stands for Time Value of Money). The TI83 has a great TVM Solver in the Apps/Finance menu.
Hit "Apps" then "Finance", choose TMV Solver. Hit Enter
• N is the number of payments • I% is the annual interest rate • PV is the present value of the loan • PMT is the payment. • FV is the future value of the loan • P/Y is the payments per year. • CY is the compounding periods per year.
NOTES:• if a variable is not being used in a question, or it is being solved for,
put in zero for its value.• For our purposes we will always leave PMT at END• To solve for a variable: Make sure you put in 0 for its' value.• Scroll down to the variable you want to solve for and hit "Enter".
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Examples:
1. Consider Lars, who borrowed $12000 from a bank at 5% compounded monthly to purchase a new snowmobile. The bank requires him to pay $350 per month until the loan is paid off. A) How long it will take to pay off at least half of the loan?
B) How long it will take to pay off of the loan?
To solve for N, we use the arrow keys to navigate to N and select SOLVE (press ALPHA then ENTER).
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Number of Months to Pay off Loan_________________
Total Amount Paid =_____________________________
Approximate Interest Paid = ______________________
Exact amount of interest paid =____________________
C) How much interest will Lars have paid by the time the loanis paid off? (Both estimated value and exact value – to find exact amount of interest we have to use our Finance App.)
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2. When you were born your grandparents deposited $5,000 in a special account for your 21st birthday. The interest was compounded monthly at 5%. A) How much will it be worth on your 21st birthday?
B) Suppose they also added $ 10 every month. How much will it be worth on your 21st birthday?
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3. A bank offers a mortgage rate of 3.75% compounded semiannually for a 25 year period. Connie purchases a $300 000 house with a 10% down payment. A) Use TMV solver to determine her monthly payment.
B) How much interest does she pay?
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4. Brittany takes out a loan for $100 000 at 6% annual interest. She takes 20 years to repay the loan.A) Use a financial application to determine the amount of each monthly
payment.
B) How much interest will she have paid at the end of the 20 years?
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5. Which is the better option? Explain.
Option 1: Cost of a mortgage is $300 000, interest rate 2.5%, monthly payments, 25 year amortization.
Option 2: Cost of mortgage is $300 000, interest rate is 3.5%, monthly payments, 20 year amortization.
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6. Tyler purchases a $2200 mountain bike. He has two payment options:• He can pay $2200 in cash.• He can pay a $20 administration fee, and then make monthly payments
at 8% compounded monthly for one year.
Determine how much more he will pay if he uses the second option.
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7. Mr. Lovell decided to purchase a $30000 first edition of Schindler’s List by Thomas Keneally. His bank offers to loan him the money (because he is a poor teacher!) for 5 years. He must make monthly payments of $605.04.
A) Determine the rate of interest if it is compounded semiannually.
B) Determine when the loan is half paid;
C) Determine the total amount of interest paid;
D) Determine the amount of money from the 36th payment that went towards the principal.
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Using the TVM Solver, complete the following table:
Describe what happens as the loan periods increase.
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Using the TVM Solver, complete the following table:
Describe what happens as the compounding period increases.
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A note about accelerated biweekly payments
Another option that banks often offer to the borrower is the option to pay back a loan with accelerated biweekly payments. Consider a loan of $100000 in which a person has a $600 per month payment. The interest is compounded annually at 5%. Using our TVM Solver, we see that it takes about 280 months (or 23.33 years) to pay off the loan, with total interest paid being $67695.50. In the span of one year, this person would pay 12 x $600 = $7200.
If this person decided to go on a biweekly payment plan, we would determine his payment per period by dividing $7200 by the 26 periods:
Even though this person is paying the exact same money per year, he will save interest charges and lower his amortization date – the time taken to pay off a loan – because he is saving on interest charges by paying every two weeks instead of waiting until the end of the month. Using our TVM Solver, we see it takes 605 periods, which is equivalent to 1210 weeks (or 23.27 years). The total interest is $67356.53. The person has not saved much time or much money considering the length of time of the loan.
An accelerated biweekly payment combines the two types of payments. The person pays half of the original monthly loan payment (in this case $300) every two weeks. At this rate, the loan will be paid off in 525 periods. This is 1050 weeks or 20.19 years. This saves over 3 years of paying off a loan. The total interest paid is $57274.12, which is a savings of over $10000!
The lesson – pay off your loans as quick as possible!