Question

(Picture attached below!)


Solve for t.

@jim_thompson5910

Answer 1

l=prt is for simple interest and NOT compound interest

Answer 2

:(

Answer 3

A = P*(1+r/n)^(n*t)

is for compound interest

Answer 4

4,227.29*(1+0.049/n)^(n*t) = A

**I'm confused on "n" and "A".
*I know we're solving for "t".

Answer 5

we're compounding monthly, so n = 12

that means we're compounding the interest 12 times per year

Answer 6

so every month, we're adding a small portion of the principal to the account

when the next month rolls along, the account is slightly bigger which means that when we calculate interest for this next month, it'll be slightly higher

Answer 7

here's an example

say we start out with $100

now let's say we have an annual interest rate of 12%. Yes it's pretty high, but it's easy to work with

Answer 8

4,227.29*(1+0.049/12)^(12*t) = A
What about "A" ?
:/

Answer 9

the monthly interest rate is 12%/12 = 1%

ok so we start out with $100

month 1 comes to a close and we'll add 1% of $100 = 0.01*100 = 1 dollar

so at the end of month 1, we'll have $101 in the account

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then month 2 rolls around and we take 1% of $101 to get 0.01*101 = 1.01

So we'll have 101+1.01 = 102.01 dollars in the account after month 2

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This pattern continues

Answer 10

A is the final amount in the account after t years

in this case, we want the amount to be $9000

Answer 11

and we're solving for t

Answer 12

So much math...
4,227.29*(1+0.049/12)^(12*t) = 9, 000 ?

Answer 13

good, now solve for t

Answer 14

yeah it's a lot but with a lot of practice, you'll get the hang of it

Answer 15

t= 15. 453

Answer 16

correct

Answer 17

Now I'm just confused on whether it's C or D..?

Answer 18

break up 15. 453 to get 15 + 0.453

Answer 19

the 15 refers to 15 whole years

Answer 20

the 0.453 is a piece of a whole year

0.453*12 = 5.436

So 0.453 years = 5.436 months

Answer 21

Ah, answered my next question!^

Thank you !! (:

Answer 22

so apparently they rounded up to 6 months (makes sense to clear that hurdle)