The Jones hope to accumulate $12000 for a sunroom over the next 6 yrs. How much would they need to invest right now at 3.9% compounded quarterly to reach goal?
Please help
Here are several pieces that explain how to compute compound interest.
http://www.bing.com/search?q=computing+compound+interest&form=EDGNTC&qs=PF&cvid=41403759967741bbbac848a42db2f4f1&pq=computing%20compound%20interest
12000(1+0.039/4)^4(6)
12000(1.00975)^24=15146.56
is this correct
To calculate the amount the Jones need to invest right now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, the accumulated amount they desire is $12,000, the annual interest rate is 3.9% (or 0.039), the interest is compounded quarterly (n = 4), and the investment period is 6 years.
Substituting these values into the formula, we can solve for P:
$12,000 = P(1 + 0.039/4)^(4*6)
Simplifying the equation further:
$12,000 = P(1 + 0.00975)^(24)
$12,000 = P(1.00975)^24
Now, divide both sides of the equation by (1.00975)^24 to isolate P:
P = $12,000 / (1.00975)^24
Using a calculator, we find:
P ≈ $9,548.24
Therefore, the Jones would need to invest approximately $9,548.24 right now at a 3.9% interest rate compounded quarterly to reach their goal of $12,000 in 6 years.
To determine how much the Jones would need to invest right now at a 3.9% quarterly compounded interest rate in order to accumulate $12,000 over the next 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($12,000)
P = the principal amount (the initial investment we are trying to find)
r = the annual interest rate (3.9%)
n = the number of times interest is compounded per year (4, since it is compounded quarterly)
t = the number of years (6)
Plugging in the given values, we can solve for P:
$12,000 = P(1 + 0.039/4)^(4*6)
First, let's simplify the equation within the parentheses:
$12,000 = P(1.00975)^(24)
Next, let's raise 1.00975 to the power of 24:
$12,000 = P(1.254148)
Finally, divide both sides by 1.254148 to solve for P:
P = $12,000 / 1.254148
P ≈ $9,570.13
Therefore, the Jones would need to invest approximately $9,570.13 right now at a 3.9% quarterly compounded interest rate in order to accumulate $12,000 over the next 6 years.