Student, House, and Car Loans

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Maude Hicks
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1 Student, House, and Car Loans words with mort in them are often deadly& among the deadliest are mortgage and amortization: mortgage= death pledge amortize a debt=to kill the debt events described all actually happened, and the same language is purposely used. Real-life considerations can be ill-defined and have multifaceted aspects. Whether it is counting the number of stars, understanding why the Franklin funds never earns 5%, or many of the other concepts we will consider, many cases require the critical and creative analysis of a variety of interpretations in order to fully consider the implications. when our own future is at stake, most of us want to use every effective approach we can. Mathematics is not the only way to approach decisions, but the reasoned strategies are powerful tools.

2 Do you have a student loan? a) yes b) no c) other Take our your real-life rates assignment a) What is the student loan rate? b) What is the car loan rate? Notice the loan rates are higher than the savings rates, factoring in risk. We ll need the rates again in the car lab.

3 Loan Payments lender earns what it could elsewhere, we pay in installments: lump sum of loan = periodic payment of our installments

4 Loan Payments lender earns what it could elsewhere, we pay in installments: lump sum of loan = periodic payment of our installments loan (1 + r) n = installment payment((1 + r)n 1) r = periodic rate (like.05 r 12 ) n = # times actually compounded (like 120 or 360)

5 Loan Payments lender earns what it could elsewhere, we pay in installments: lump sum of loan = periodic payment of our installments loan (1 + r) n = installment payment((1 + r)n 1) r = periodic rate (like.05 r 12 ) n = # times actually compounded (like 120 or 360) 1 solve for payment by reciprocals, exponents, and distribution. First mult both sides by reciprocal r (1+r) n 1

6 Loan Payments lender earns what it could elsewhere, we pay in installments: lump sum of loan = periodic payment of our installments loan (1 + r) n = installment payment((1 + r)n 1) r = periodic rate (like.05 r 12 ) n = # times actually compounded (like 120 or 360) 1 solve for payment by reciprocals, exponents, and distribution. First mult both sides by reciprocal (1 + r) n installment payment = loan r (1 + r) n 1 r (1+r) n 1

7 Loan Payments lender earns what it could elsewhere, we pay in installments: lump sum of loan = periodic payment of our installments loan (1 + r) n = installment payment((1 + r)n 1) r = periodic rate (like.05 r 12 ) n = # times actually compounded (like 120 or 360) 1 solve for payment by reciprocals, exponents, and distribution. First mult both sides by reciprocal (1 + r) n installment payment = loan r (1 + r) n 1 r (1+r) n 1 2 reduce further by multiplying both the numerator and denominator by (1 + r) n so the top reduces by exponents:

8 Loan Payments lender earns what it could elsewhere, we pay in installments: lump sum of loan = periodic payment of our installments loan (1 + r) n = installment payment((1 + r)n 1) r = periodic rate (like.05 r 12 ) n = # times actually compounded (like 120 or 360) 1 solve for payment by reciprocals, exponents, and distribution. First mult both sides by reciprocal (1 + r) n installment payment = loan r (1 + r) n 1 r (1+r) n 1 2 reduce further by multiplying both the numerator and denominator by (1 + r) n so the top reduces by exponents: (1 + r) n (1 + r) n = loan r (1 + r) n ((1 + r) n 1) = loan r 1 (1 + r) n (1 + r) n (1 + r) n

9 Loan Payments lender earns what it could elsewhere, we pay in installments: lump sum of loan = periodic payment of our installments loan (1 + r) n = installment payment((1 + r)n 1) r = periodic rate (like.05 r 12 ) n = # times actually compounded (like 120 or 360) 1 solve for payment by reciprocals, exponents, and distribution. First mult both sides by reciprocal (1 + r) n installment payment = loan r (1 + r) n 1 r (1+r) n 1 2 reduce further by multiplying both the numerator and denominator by (1 + r) n so the top reduces by exponents: (1 + r) n (1 + r) n = loan r (1 + r) n ((1 + r) n 1) = loan r 1 (1 + r) n (1 + r) n (1 + r) n 1 installment payment = loan r 1 (1 + r) n =

10 Loan Payments lender earns what it could elsewhere, we pay in installments: lump sum of loan = periodic payment of our installments loan (1 + r) n = installment payment((1 + r)n 1) r = periodic rate (like.05 r 12 ) n = # times actually compounded (like 120 or 360) 1 solve for payment by reciprocals, exponents, and distribution. First mult both sides by reciprocal (1 + r) n installment payment = loan r (1 + r) n 1 r (1+r) n 1 2 reduce further by multiplying both the numerator and denominator by (1 + r) n so the top reduces by exponents: (1 + r) n (1 + r) n = loan r (1 + r) n ((1 + r) n 1) = loan r 1 (1 + r) n (1 + r) n (1 + r) n 1 installment payment = loan r 1 (1 + r) n = loan r 1 (1 + r) n

11 Loan Payments and Amortization loan amount r = loan payment 1 (1 + r) n total paid= payment # times compounded - overpayment total interest = total paid - loan

12 Loan Payments and Amortization loan amount r = loan payment 1 (1 + r) n total paid= payment # times compounded - overpayment total interest = total paid - loan interest each period on a loan is computed just as in savings: account balance periodic rate but now we pay it back rather than earn it

13 Loan Payments and Amortization loan amount r = loan payment 1 (1 + r) n total paid= payment # times compounded - overpayment total interest = total paid - loan interest each period on a loan is computed just as in savings: account balance periodic rate but now we pay it back rather than earn it amortization table month Payment Interest Paid Principal Paid Loan Balance

15 Dear Sarah J Greenwald At this time you have a choice of repayment terms for your student loan $ at 8% compounded monthly: Graduated Repayment Plan # PMTS PMT AMT Level Payment Plan # PMTS PMT AMT total $ total $

Section 5.1 Simple and Compound Interest

Section 5.1 Simple and Compound Interest Question 1 What is simple interest? Question 2 What is compound interest? Question 3 - What is an effective interest rate? Question 4 - What is continuous compound