Question

find the amount accumulated when $300 is deposited quarterly for 10 years at 6%/year in an account containing $1500 at the start. assume end of period deposits and compounding at the same intervals as deposits.

Answer 1

use the annuity formula

Answer 2

\(\large FV = C\bullet \frac{(1+i)^{nt}-1}{i}\)

Answer 3

does that look familiar ?

Answer 4

oh yes!

Answer 5

so c is 1500 right

Answer 6

Nope,

C = periodic cash payments = 300

Answer 7

forget about 1500 for now. we can deal wid it separately

Answer 8

oh my bad

Answer 9

its there to trick us :) figure out other variables

Answer 10

\[300*\frac{ 1+0.06/12^{12*10}-1 }{ 0.06/12 }\]

Answer 11

@ganeshie8 ?

Answer 12

are we depositing 300 every month ?

Answer 13

oh no quarterly equaling 4

Answer 14

yes, that means \(\large n = 4\) right ?

Answer 15

yes

Answer 16

which makes \(\large i = \frac{r}{n} = \frac{0.06}{4}\)

Answer 17

correct so then \[300*\frac{ 0.06/4^{4*10}-1 }{ 0.06/4 }\]

Answer 18

Looks good !

Answer 19

So thats the future value for $300 periodic payments.
simplify it

Answer 20

8.97?

Answer 21

what do u mean 8.97 ?

Answer 22

whoops

Answer 23

$300 every quarter for 10 years became 8.97 ? ha

Answer 24

hahah oh god my bad

Answer 25

u may use wolfram as ur calculator :
http://www.wolframalpha.com/input/?i=++300*%5Cfrac%7B%281%2B%5Cfrac%7B0.06%7D%7B4%7D%29%5E%7B4*10%7D-1%7D%7B%5Cfrac%7B0.06%7D%7B12%7D%7D+

Answer 26

oh ok

Answer 27

i tried entering into TI-84 calc lol

Answer 28

thats a pain in d a.. .lol
use wolfram always for these lengthy calculations :)

Answer 29

next look at the starting $1500

Answer 30

if only they'd let us on exams! haha and ok

Answer 31

can u find its future value ?

Answer 32

whats the formula again? fv=?

Answer 33

1500 fixed amount, 6% annual interest rate
for 10 years
quarterly compounding

Answer 34

for fixed deposit the Future Value formula is :

\(FV = PV * (1+i)^{nt}\)

Answer 35

\(\large FV = 1500*(1 + \frac{0.06}{4})^{4*10}\)

Answer 36

simplify

Answer 37

15920.45

Answer 38

that looks way too much. check once agian..

Answer 39

damn Calc lol let me try on alph

Answer 40

2721.02

Answer 41

Correct !
add this to the previous money.

total = ?

Answer 42

2721.02+48841.10=51562.12

Answer 43

thats right !
u may check it wid woflram again :
http://www.wolframalpha.com/input/?i=++300*%5Cfrac%7B%281%2B%5Cfrac%7B0.06%7D%7B4%7D%29%5E%7B4*10%7D-1%7D%7B%5Cfrac%7B0.06%7D%7B12%7D%7D+%2B+1500%281%2B0.06%2F4%29%5E%284*10%29

Answer 44

awesome so that'd be the answer?

Answer 45

yup !

Answer 46

awesome, how i hate math at times haha

Answer 47

thank you!

Answer 48

ikr.. financial algebra can make u feel that lol...

Answer 49

but actually only handful of formulas are there to remember

Answer 50

haha yeah formulas are everywhere

Answer 51

if u memorize them and are able to pull them at will when required... u wil feel comfortable

Answer 52

have fun :)

Answer 53

thank you ill definitely be studying them

Answer 54

np :)