Suppose that $575.75 is invested in a savings account with an APR of 12%
compounded monthly. What is the future value of the account in 5 years?
Type your answer in the box below. Round your answer to 2 decimal places.
Having homework problems can’t seem to figure out this question could someone help me out please!!!
Applying the formula A = P(1+r/n)^(nt) you have
575.75(1 + 0.12/12)^(12*5) = _____
Sure, I'd be happy to help you out! Math problems can be quite tricky, but fear not, I'm here to lend you a hand... or should I say a clown nose? Let's solve this together, shall we?
To calculate the future value of the savings account, we'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the initial investment ($575.75 in this case)
r = the annual interest rate (12% or 0.12 as a decimal)
n = the number of times interest is compounded per year (monthly, so 12 in this case)
t = the number of years (5 in this case)
Now let's plug in the values and crunch some numbers:
A = 575.75(1 + 0.12/12)^(12*5)
Lemme grab my calculator real quick, and... ta-da! The future value of your account after 5 years is approximately $979.95.
Remember to round your answer to 2 decimal places! I hope this helps, and don't hesitate to ask if you have any more questions. Good luck with your homework!
To calculate the future value of the account, we can use the formula for compound interest:
\[A = P\left(1 + \frac{r}{n}\right)^{nt}\]
Where:
A = Future value
P = Principal amount (initial investment)
r = Annual interest rate as a decimal
n = Number of times the interest is compounded per year
t = Number of years
In this case, we are given:
P = $575.75
r = 12% = 0.12
n = 12 (compounded monthly)
t = 5 years
Plugging these values into the formula, we have:
\[A = 575.75\left(1 + \frac{0.12}{12}\right)^{(12)(5)}\]
Simplifying the expression inside the parentheses:
\[A = 575.75(1 + 0.01)^{(12)(5)}\]
\[A = 575.75(1.01)^{60}\]
Calculating the expression inside the parentheses:
\[A = 575.75(1.01)^{60} \approx 734.77\]
Therefore, the future value of the account in 5 years is approximately $734.77 when rounded to 2 decimal places.
Sure, I can help you with this problem! To find the future value of an investment with compound interest, we can use the formula:
\[A = P(1 + r/n)^(n*t)\]
Where:
- A is the future value of the investment
- P is the principal amount (the initial investment)
- r is the annual interest rate (expressed as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the principal amount (P) is $575.75, the annual interest rate (r) is 12% (or 0.12 as a decimal), the interest is compounded monthly (n = 12), and we want to find the future value after 5 years (t = 5).
Substituting the values into the formula, we have:
\[A = 575.75(1 + 0.12/12)^(12*5)\]
Now, let's calculate this expression step by step:
1. First, simplify the expression inside the parentheses:
\[1 + 0.12/12 = 1 + 0.01 = 1.01\]
2. Next, calculate the exponent:
\[12*5 = 60\]
3. Now, substitute these values back into the original formula and calculate:
\[A = 575.75(1.01)^{60}\]
Using a calculator, we find that \(A \approx 1053.15\).
So, the future value of the account after 5 years is approximately $1053.15.