Question

?(Compound

value solving for

r?)

At what annual rate would the following have to be? invested?

a.

?$500500

to grow to

?$1 comma 569.211,569.21

in

1212

years

b.

?$290290

to grow to

?$577.84577.84

in

88

years

c.

?$4747

to grow to

?$691.55691.55

in

2222

years

d.

?$204204

to grow to

?$248.20248.20

in

55

years

Answer 1

We use the formula:

A=P(1+r/100)^n

where

A=future value

P=present value

r=rate of interest

n=time period.

1.

a.

1569.21=500(1+r/100)^12

(1569.21/500)^(1/12)=(1+r/100)

(1+r/100)=1.10

r=(1.10-1)*100

=10%

b.

577.84=290(1+r/100)^8

(577.84/290)^(1/8)=(1+r/100)

(1+r/100)=1.09

r=(1.09-1)*100

=9%

c.

691.55=47(1+r/100)^22

(691.55/47)^(1/22)=(1+r/100)

(1+r/100)=1.13

r=(1.13-1)*100

=13%

d.

248.20=204(1+r/100)^5

(248.20/204)^(1/5)=(1+r/100)

(1+r/100)=1.04

r=(1.04-1)*100

=4%