Question

Tia is investing $ 2500 that she would like to grow to $ 6000 in 10 years, at what annual interest rate compounded quarterly must Tia invest her money? I know that PV = 6000 A= 2500 i = ? n = 40 My teacher gave us the formula PV = A (1+i) -n I am having troubles isolating i, I am not sure how to get to the right answer

Answer 1

use the compound interest formula

A = P(a + r/t) ^ nt

where P is the starting amount , r = annual rate in decimal form, t = number of times interest is pais in a year and n = number of years

Answer 2

So how would I get rid of thee exponent? square root?

Answer 3

plug in the given values first

6000 = 2500( 1 + r/4)^40

Answer 4

Im confused as to why it is r/4

Answer 5

is it because i = r/N

Answer 6

because the interest is paid 4 times a year
r = annual rate

Answer 7

That is what they ask for - annual rate.

Answer 8

alright that makes sense

Answer 9

so if we divide both sides by 2500 to isolate the exponent part we get

(1 + r/4)^40 = 2.4

now take logs of both sides

Answer 10

why do we log?

Answer 11

Sorry I just want to make sure I understand this well so I can do it again later

Answer 12

- that gets rid of the exponenents

Answer 13

alright so I log the other side

Answer 14

the side witht he 2.4

Answer 15

is this inverse log or just log?

Answer 16

what? I somehow lost my post!!???

Answer 17

take logs - u can use natural logs:-

ln (1 + r/4)^40 = ln 2.4

by law of logs

40 ln (1 + r/4) = ln2.4

ln ( 1 + r/4) = ln2.4 / 40


ok so far?

Answer 18

I think so, so by doing log I will be getting rid of the 40 exponent?

Answer 19

yea

Answer 20

Alright that makes sense

Answer 21

so I have 0.380211242 = 1+ r/4

Answer 22

now work out right side

ln (1 + r/4) = 0.0218867

Answer 23

Wait how is it 0.021, Im not sure why Im getting a diffrerent number

Answer 24

0.021 = ln (1 + r/4)

now you can use inverse logs

Answer 25

you should use 0.0218867 to get accurate result

Answer 26

use the e^x key on ur calculator - remember we are using natural logs

Answer 27

Alright I think I understand now

Answer 28

( 1 + r/4) = e^0.021887

Answer 29

good
you should get a result which is between 8 and 9%

Answer 30

Aim to isolate the expression you want to evaluate and then takes logs

note we use the log law log a^n = n log a

Answer 31

It's nice to deal with someone who wants the learn rather than just get an answer.

Answer 32

Alright I think that should be alright then, thank you very very much!!

Answer 33

yw