Today in Precalculus• Go over homework• Need a calculator• Notes: Annuities (Future Value)• Homework

Annual Percentage Rate (APR)

• Often accounts are given an APR.• This assumes the interest is compounded

only once a year.• To determine the compounding interest rate

divide the APR by the number of times in a year the interest is compounded.

Annuities• A sequence of periodic payments instead of a

lump sum.• Ordinary annuities are when the deposits are

made at the end of each period at the same time the interest is posted in the account.

1 1niFV R

i

FV: future valueR: 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

(25 4)(1 .0683/ 4) 1250.0683/ 4

FV

=$64,952.14

Given APR and interest is compounded quarterlyso divide i by 4

Betsy invested $250 × 4 × 25= $25,000 So she made $64,952.14 - $25,000 = $39,952.14 in interestwhich is a return of 160% on her investment.

Example 2

(15 2)(1 .0739 / 2) 1300.0739 / 2

FV

=$15,993.37

Given APR and interest is compounded twice a yearso divide i by 2

Example 3

15,000=73.919RR=$202.92Josh needs to deposit $202.92 each month

(12 5)(1 .0823/12) 115,000.0823/12

R

Given APR and interest is compounded monthlyso divide i by 12

Homework• Pg 341: 13-16, 47-50• Chapter 3 test: Wednesday, January 20