Question

Can someone tell me what I should do for this problem? I would really appreciate it.

Answer 1

well you could multiply 90,000 by 0.046 then take 221,200 and divide the sum bit. I hope this is right (mathematics isn't my strong point)

Answer 2

by it^

Answer 3

@AZ can you help me?

Answer 4

Sure! Do you know the formula for compound interest?

Answer 5

@AZ i know how to find the rate but other than that i'm lost

Answer 6

\(\Large A = P(1 + \frac{r}{n})^{nt} \)

so A = 221,200
P = 90,000
r = 4.6% but first you have to make it as a decimal
n = 1 since we're compounding each year
t = ?? what we're solving for

Answer 7

can you plug in the numbers and solve for t

Answer 8

P is the principle amount which is what you start off with- the 90,000

the rate or r is 4.6%
t is time
n is the number of times you compound it

A is the final amount including interest

Answer 9

@AZ alright i'm trying it now

Answer 10

@Az I got it. thank you!

Answer 11

Perfect! Let me know if you want me to check your answer :)

Answer 12

@AZ it would be 20 right? 21's to much

Answer 13

That's correct haha

but did you go plugging in numbers?

Answer 14

@AZ yes i did

Answer 15

you don't need to tag me each time haha, I get a notification each time you reply but you didn't need to brute force it

Answer 16

so let me show you how to calculate it using the formula

Answer 17

oops sorry. thanks for the help tho <3

Answer 18

you plugged in the numbers I'm sure and got

\(\large A = P(1 + \frac{r}{n})^{nt}\)

\(\large 221,200 = 90,000(1 + \frac{0.046}{1})^{1t}\)

\(\large 221,200 = 90,000(1 +0.046)^{t}\)

Answer 19

yeah that's what i got

Answer 20

\(\large 221,200 = 90,000(1.046)^{t}\)

and then we divide 90,000 on both sides

\(\large 2.4577 = (1.046)^{t}\)

Answer 21

following along still?

Answer 22

yes i am

Answer 23

so now you have to know that if we take the natural log on both sides, we can bring down that exponent

\( ln(a^b) = b ~ln(a)\)

so

\( \large ln(2.4577) =ln( (1.046)^{t})\)

and we get

\( \large ln(2.4577) =t~ ln(1.046)\)

and now to solve for 't'

you just divide ln(1.046) on both sides

Answer 24

does that make sense now?

Answer 25

yes thank you

Answer 26

perfect so basically

t = ln(2.4577) / ln(1.046)

and ta-da

that's all

Answer 27

you're a life saver. i can not thank you enough for your help

Answer 28

of course! it was my pleasure :)