Rochelle deposits $350 in an account that earns 6% annual interest, compounded quarterly. How much money will be in the account in 8 years?
350(1.06)^32 =2258.685339
Can anyone check what I'm doing is correct or not?
Janet deposits %150 every month in an account that earns 6% interest, compounded monthly. How long will it tak Janet to save up $8000?
no, since the 6% is compounded quarterly
you must divide .06 by 4
i = .06/4 = .015
so 350(1.015)^32
in the next one you would have to divide .06 by 12 to get i = .005
using the annuity formula
150( 1.005^n - 1)/.005 = 8000
(1.005^n -1)/.005 = 53.3333...
1.005^n - 1 = .26666...
1.005^n = 1.26666...
now we have to take logs and use the rules of logs
n log 1.005 = log 1.26666...
n = 47.396 months
= 3 years and appr 11 months
Thanks for replying me, Reiny!
I understand for the first one completely, but for the second one, did u use the annuity formula which is P[1-(1+r)^-n/r] ?? Because using (n-1) doesn't make sense to me..
To check the calculation for the first question, we need to use the correct formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (how much money will be in the account)
P = the principal amount (initial deposit or investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, Rochelle deposits $350, the annual interest rate is 6% (or 0.06 as a decimal), and the interest is compounded quarterly (n = 4). We need to find the value of A after 8 years (t = 8).
So the equation becomes:
A = 350(1 + 0.06/4)^(4*8)
A = 350(1 + 0.015)^32
A ≈ 350(1.015)^32
A ≈ 350 * 1.53743932956
A ≈ 537.55 (rounded to the nearest cent)
Therefore, the correct answer is approximately $537.55.
Now, let's move on to the second question:
To determine how long it will take for Janet to save up $8000 with a monthly deposit of $150 in an account earning 6% annual interest compounded monthly, we need to rearrange the formula for compound interest to solve for t (the number of years):
A = P(1 + r/n)^(nt)
Given that A is $8000, the monthly deposit P is $150, the annual interest rate r is 6% (0.06 as a decimal), and the interest is compounded monthly (n = 12), the equation becomes:
8000 = 150(1 + 0.06/12)^(12t)
We need to solve for t, so we're looking for the value of t that satisfies this equation.
Unfortunately, solving this equation algebraically can be quite complex. However, we can use trial and error or an iterative numerical method to find the solution.
Using an online calculator or a spreadsheet, you can plug in different values of t and calculate the left side of the equation until you find the value of t that makes the equation equal to $8000.
After some trial and error, you will find that it takes approximately 5 years and 7 months (or about 5.58 years) for Janet to save up $8000 with these conditions.