Question

@hartnn

Answer 1

Find the compound amount at the end of 10 years on an original principal of $200 at 4% when compounded annually.

Answer 2

know the formula?

Answer 3

I think so.
\(\large P(1 + \frac{r}{n})^{n(t)}\)

Answer 4

so
P =200
n =10
r = 4% = 0.04

just plug in

Answer 5

Okay give me a moment while I do this problem :)

Answer 6

are you sure its r/n ?

Answer 7

That's what it says in here:

Answer 8

aah
its nt
not n(t)

Answer 9

I don't understand the difference.

Answer 10

t = number of years = 10

Answer 11

and what would n be?

Answer 12

n = the number of times that interest is compounded per year = 1

Answer 13

okay so if it said compounded semi-annually then n would be 2 right?

Answer 14

exactly!

Answer 15

oh okay. so let me just evaluate it and make sure my answer with you.

Answer 16

so when i do (1.004)^10 i get a decimal. am i supposed to get that?

Answer 17

yes

Answer 18

so do i round it or something?

Answer 19

so i go my answer to be \(\approx\) $208.15

Answer 20

*got

Answer 21

you took 0.004

4% is actually 0.04

Answer 22

Oh I realized my mistake! Ok just give me like one more minute :)

Answer 23

sure

Answer 24

I get \(\approx\) $296.05

Answer 25

\(\huge \checkmark \)

Answer 26

But the answer key says that it's supposed to be $295.80. I don't know why.

Answer 27

nah, we are correct :)

Answer 28

Okay!

Can you help me with a couple more please? I new to this topic

Answer 29

same type?

if you try on your own first, then i will be glad to help :)

Answer 30

What time is required to double a certain amount
1) compounded annually at 6%
2) compounded continuously at 6%

I don't know what they're saying in here .I just need to understand what they are asking for and I hope that I can do the rest.

Answer 31

you have amount x,
you want to double it
so your new amount = 2x

Answer 32

A = 2x
P =x

Answer 33

annually mean n =1
r is given, only t is unknown

Answer 34

tf is compounded "continuously" ?? :P

Answer 35

i meant 'what is compounded continuously' ? :P

Answer 36

I have no idea.

Answer 37

What do you mean by 'A'. Is that what P(1 + r/n)^n(t) would equal to?

Answer 38

yes

Answer 39

got it
http://www.mathwarehouse.com/compound-interest/continuously-compounded-interest.php

Answer 40

what do the mathematically constant 'e' mean?

Answer 41

https://en.wikipedia.org/wiki/E_(mathematical_constant)

Answer 42

I am sorry but I don't understand. I am only in eighth grade trying to take Algebra I classes :(

Answer 43

take e=2.718

Answer 44

okay. so for that question when it says compounded continuously would my equation be...

Answer 45

you got the 1st one?

Answer 46

not yet. ok let's do the first one

Answer 47

2x = x(1 + 0.06/1)^1(t)

Answer 48

Is this set-up correct?

Answer 49

yesss

Answer 50

okay.
2x = x(1.06)^t

Answer 51

How would I solve for t if I have two variables?

Answer 52

divide x on both sides

Answer 53

okay so x = 1.06^t

Answer 54

no
2x/x = 2

Answer 55

i am so dumb.

Answer 56

2 = 1.06^t

Answer 57

yes

Answer 58

may i get a hint as to what i should do next? does have to do something with roots?

Answer 59

you can use calculators, right?

Answer 60

take log on both sides

Answer 61

yes

Answer 62

ok.
so do i do log(2) and log(1.06)?

Answer 63

@hartnn

Answer 64

yes

Answer 65

ok.

Answer 66

log(2) \(\approx\) 0.3
log(1.06) \(\approx\) 0.03

Answer 67

What do I do after?

Answer 68

log 2= t log 1.06

so t = log 2/ log 1.06

Answer 69

so 0.3/0.03 = t ?

Answer 70

t = 10

Answer 71

yeah

Answer 72

yay!

can we do the compounded continuously part now?

Answer 73

yes

Answer 74

log 1.06 is 0.0253

Answer 75

calculate t again

Answer 76

okay

Answer 77

0.3/0.0253 = 11.85

Answer 78

which would be 11.9 yrs.

Answer 79

which place value do we round it to after doing the log?

Answer 80

atleast 2 digits after decimal

Answer 81

11.9 is very close to 12...both will be acceptable

Answer 82

okay. so for number 2

Answer 83

A = 2x
P = x
e = 2.718
r = 0.06
t = ?

Answer 84

2x = P(2.718)^0.06t

Answer 85

sorry 2x = x(2.718)^0.06t

Answer 86

Is that correct?

Answer 87

yes

Answer 88

okay
2 = (2.718)^0.06t

Answer 89

now how do i solve for t?

Answer 90

same
take log on both sides

Answer 91

do i take the log of 2.718 or 1.06?

Answer 92

\(\Large \log x^n = n \log x \)

\(\log 2 = \log 2.718^{0.06t} \implies \log 2 = (0.06t)\times \log 2.718\)

Answer 93

makes sense?

Answer 94

yes
log(2) = 0.301
log(2.718) = 0.434

0.301 = 0.434 \(\times\) 0.06t

Answer 95

now do i multiply 0.434 by 0.06 and then put in the t ?

Answer 96

yes, you can do that

Answer 97

0.02604t = 0.301
t = 11.6 yrs