A company will need 65,000 in 6 years to add an addition. to meet this goal the company deposits money in an account today that pays 5% annual intrest compoundded quarterly. Find the amount that should be invested to total 65,000 in 6 years.
the company should invest?
plz help . thank you sooo much .
solve for P in
P(1+.05/4)^(4*6) = 65000
still lost can you explain step by step?
Looks like you need to review your compound interest formula.
$P invested at at a rate of r, compounded n times per year for t years grows to
P(1+r/n)^(nt)
So, knowing that
(1+.05/4)^(4*6) = 1.347, you now just have to solve
1.347P = 65000
To find the amount that should be invested to total $65,000 in 6 years, you need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($65,000 in this case)
P = the principal amount (the amount to be invested)
r = the annual interest rate (5% or 0.05 as a decimal)
n = the number of times interest is compounded per year (quarterly, so 4)
t = the number of years (6 years in this case)
To solve for P, we can rearrange the formula:
P = A / (1 + r/n)^(nt)
Now, let's plug in the values:
P = 65000 / (1 + 0.05/4)^(4 * 6)
First, simplify inside the parentheses:
P = 65000 / (1 + 0.0125)^(24)
Then, calculate the exponent:
P = 65000 / (1.0125)^(24)
Finally, calculate the final result:
P ≈ $46,033.75234
Therefore, the company should invest approximately $46,033.75 to reach a total of $65,000 in 6 years.