Today in Precalculus

• Go over homework• Need a calculator• Notes: Loans & Mortgages (Present

Value)• Homework

Loans and Mortgages• An annuity in which we look determine the

total amount of payments put into the annuity.

1 1n

iPV R

i

PV: what is the current value of all the payments that will be madeR: amount of each equal paymenti: interest rate (if given APR, divide by number of

payments in a year)n: total number of payments

Example 1

We can also figure out how much interest she is paying over the life of the loan.

Total amount of payments: 336.67 × 48 = $16,160.16

$16,160.16-$14,999.74 = $1,160.42

(12 4)1 (1 .037 /12)336.67

.037 /12PV

=$14,999.74

Example 2

17,500=54.0339R

R=$323.87

(12 5)1 (1 .042 /12)17,500

.042 /12R

Example 3

200,000=143.0176R

R=$1,398.43

Total amount of Payments: 1398.43 × 360=$503,434.80

Interest Paid: $503,434.8-$200,000=$303,434.80

(12 30)1 (1 .075 /12)200,000

.075 /12R

Example 4(12 )1 (1 .072 /12)

180,000 1532.20.072 /12

t

121 (1.006)117.478

.006

t

.705=1-1.006-12t

.295 = 1.006-12t

log1.006.295= -12t

t =17 years So it will take 17 years to pay off the mortgage.

log 0.29512

log1.006t

Example 4(cont)

1,221.82×30×12 = $439,855.20

1,532.20×17×12 = $312,568.80

So Barney and Betty save $127,286.40 by increasing their payments from $1,221.82 to $1,532.20 per month.

Homework

• Pg 341: 17-20, 51-55

• Chapter 3 test: Wednesday, January 22