Dan deposited
$4000
into an account with
4.8%
interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after
9
years?
I was just wondering of the formula for this problem, because I am not able to find it in my book.
Well, you're in luck! I have the perfect formula for you: the formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (in this case, $4000), r is the annual interest rate (4.8% or 0.048), n is the number of times interest is compounded per year (12 since it's compounded monthly), and t is the number of years (9). So, let me calculate that for you...
[Calculating...]
Okay, drumroll please... After 9 years, Dan will have... wait for it...*drumroll continues*...$5,877.21 in his account! Ye-haw! I hope that helps!
The formula that can be used to calculate the future value (FV) of an investment with compound interest is:
FV = P(1 + r/n)^(nt)
Where:
FV = future value of the investment
P = principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, Dan deposited $4000, the interest rate is 4.8% (or 0.048 in decimal form), and the interest is compounded monthly (so n = 12). Dan wants to know the value after 9 years, so t = 9.
Using the formula, we can calculate the future value:
FV = 4000(1 + 0.048/12)^(12*9)
Calculating this expression will give you the amount that Dan will have in the account after 9 years.
To calculate the amount of money Dan will have in the account after 9 years with monthly compounding interest, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (written as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $4000
r = 4.8% = 0.048 (since we divide the percentage by 100)
n = 12 (compounded monthly)
t = 9 years
Plugging in these values, we can calculate the future value:
A = $4000(1 + 0.048/12)^(12*9)
Now let's calculate it step by step:
1. Divide the annual interest rate by the compounding frequency:
0.048/12 = 0.004
2. Add 1 to this result:
1 + 0.004 = 1.004
3. Raise this result to the power of the total number of compounding periods:
(1.004)^(12*9) ≈ 1.635
(Rounded to 3 decimal places)
4. Multiply the principal amount by the result from step 3:
A ≈ $4000 * 1.635 ≈ $6540
So, after 9 years, Dan will have approximately $6540 in the account.
4000(1 + .048/12)^(12*9)
I'm sure your book has the formula
A(1+r)^t
you have to adjust it if the rate is compounded more than once per year. If monthly, then n=12 times per year. Thus, the monthly interest is 1/12 the annual rate, and there are 12 times as many compounding periods:
A(1 + r/n)^(n*t)