Question

Rachel deposited $5,960.32 into a savings account with an interest rate of 4.2% compounded twice a year. About how long will it take for the account to be worth $9,000?
a. 21 years, 1 month

b. 18 years, 0 months

c. 19 years, 10 months

d. 9 years, 11 months

Answer 1

\[A=P(1+\frac{r}{n})^{nt}\]
where A is the amount after t years
P is the principal
r is the annual interest rate as a decimal (0.042 in this case)
n is the number of times per year that the interest compounded
Plugging in the given values we get:
\[9000=5960.32(1+\frac{0.042}{2})^{2t}\]
Now you need to solve for t.

Answer 2

@xoxo_devvie Are you there?

Answer 3

sorry about that. thank you so much! you show me the process? im taking online classes and dont have a teacher here with me and im trying to learn the lesson by myself

Answer 4

np. Do you need help to solve?

Answer 5

yes please

Answer 6

\[9000=5960.32(1+\frac{0.042}{2})^{2t}\]
First divide both sides by 5960.32, and add the terms inside brackets giving:
\[\frac{9000}{5960.32}=(1.021)^{2t}\]
Next take natural logs of both sides to get:
\[\ln 1.509986=2t \times \ln 1.021\]
Now divide both sides by ln 1.021 getting
\[2t=\frac{\ln 1.509981}{\ln 1.021}\]
Then dividing both sides by 2 we finally get:
\[t=\frac{\frac{\ln 1.509981}{\ln 1.021}}{2}\]

Answer 7

how do i know how to convert it into years and months to find the answer?

Answer 8

First calculate t as a decimal quantity. The years do not need conversion.Then we can convert the decimal fraction to months.

Answer 9

Use your calculator to find the value of
\[\frac{\ln 1.509986}{\ln 1.021}\]
Then divide the result by 2 to get the value of t. Can you do that?

Answer 10

one second let me see

Answer 11

i got 0.739?...

Answer 12

Did you use the natural logs function on your calculator. It is the 'ln' function.

Answer 13

i only have a basic calculator :(

Answer 14

The is a free online calculator here:
http://web2.0calc.com/
Put the cursor on the 'log' key and select 'ln' on the drop-down menu.

Answer 15

ok!

Answer 16

.391 is what i got this time?

Answer 17

Well I used the online calculator and got a correct result. Can we go through using it step by step?

Answer 18

yes!

Answer 19

Put the cursor on the 'log' key and select 'ln' on the drop down menu. What do you see in the window at the top of the calculator?

Answer 20

this is what i see

Answer 21

Great! Now enter 1.509981, followed by a closing bracket. Next click on the division key and then put the cursor on the 'log' key again and select 'ln'. Enter 1.021, followed by a closing bracket. Then click on the '=' key.

Answer 22

so the answer is 3?

Answer 23

No. When I do the operations the result is 19.8290047403184753. When this is divided by 2 the result is 9.91450237015923765. This converts to 9 years, 11 months.

Answer 24

how did you get that ?

Answer 25

oh! there we go i got it! do you think you can help me with one more?

Answer 26

Good work! Sorry I have to go now. I am sure others can help :)