Compound Interest

Section 5

Objectives

• Determine the future value of a lump sum of money

• Calculate effective rates of return• Determine the present value of a lump sum of

money• Determine the time required to double or triple

a lump sum of money

Simple Interest Formula

I = Prt

I: interestP: principal

r: ratet: time (yearly/per annum)

Payment Periods

Annually: once per yearSemiannually: twice per yearQuarterly: four times per year

Monthly: 12 times per yearDaily: 365 per year*

*Most banks use a 360-day year.

When large sums are involved, the 360-day method (known as

ordinary interest or banker's rule) yields significantly more interest to the lender. It is used by banks and commercial organizations.

Compound Interest

Interest paid on principal and previously earned interest

A credit union pays interest of 8% per annum compounded

quarterly on a certain savings plan. If $500 is deposited in such

a plan and the interest is left to accumulate, how much is in the

account after 1 year?

Compound Interest Formula

A: Future valueP: Present value

n: Number of times compounded per year

A P 1r

n

nt

Page 541 #3

Continuous Compounding

The number of times the interest is compounded is increased

without bound.

A = Pert

Page 541 #11

Effective Rate of Interest

The equivalent annual simple interest rate that would yield the same amount as compounding

after one year.

See pages 537 and 538

Page 541 #23

Present Value Formulas

P = Aert

P A1r

n

nt

Page 541 #13

Page 541 #25

Page 542 #29

Pages 541-542(5, 7, 9, 15, 17, 19, 21, 27, 33, 35, 49)