il**pu*d

\rtt*rm+

WS N*ffir

Formulas for Compound lnterest

After , years, the balance, A, in an account with principal P and annuai

inter.est

rate i' (in decimal form) is given by the follorving formulas:

year. t r \r, 1. For rL compounding periods per year: A : P[1 * ;) 2. For continuous compounding: A : Pe'l

n is the nr.rmber of compounding periods per

S10,000 is invested at an annual interest rate' of 3o/o

for

5 years.

;^ff;; de3

Find the balance after 5 years for the

different compounding periods.

a) yearly (n:1)

'

b)

semi-a:rnually (n:2)

c)

quarterly (n=4)

d) monthly (n:12)

e) daily (n:365)

f)

continuously

,' How long would it take for an invqstm.ent of $1 to reach at a:e an:eual interest rate of 100yo2

$2-71.8

if

the investrnent is compounded continuousiy

1)

:Find tfre arcurnulated vnlue of an investrrient sf $S*fi(] . for It) )reffrs at an interest rate *f 6.5q'" ii'the money is n,. c'*mprurnded xerniannuallS,,; I*. cmrnpou*"ded quarterly; s" **m pCIn n d sd mr-l r: thly ; d" c n nlp r:lr.r nded c*ntinur"rustry"

2)

$uppos* thmt vou havr $l?-fifl{) t* invest. Which iuvestmcnt yields the great*f, returlr *ver 3 years: ??i, cnrnp*unded m*nthly *r 6.fi5% c$nrp('und*d continuouslv?

3)

Yeiu have $tr#,fifi# to invcst, One l:rank pxys 5% interest c$lnpfiunded qu*rterly ar::cl n sc*mnd hank pavs 4.5(Hi interxst ct}rr}prundrd m*nth}1r s. lJ*e ttre f*rrnuln f*r rcnltr]rxrfid interest tn write a functinn f'nr thn [:*lanre in earh trank at nlry tims t,. h. Use a grapfring utilit,v ter. graph *:oth functions in nn appr*prlate viewing rectangle. Based on the grapfrs, whictr hank *ff*rs the better return fln your mt:ney?