A company will need $35000 in 6 years for a new addition. To meet this goal the company deposits money in an account today that pays 6% annual interest compounded quarterly. Find the amount that should be invested to total $35000 in 6 years. The company should invest
PRT Formula
35,000(.06)(6years) = 1260
To find the amount that should be invested today, we 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 (the amount to be invested)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Given:
A = $35,000
r = 6% = 0.06 (as a decimal)
n = 4 (quarterly compounding)
t = 6 years
Substituting the given values into the formula, we can solve for P:
$35,000 = P(1 + 0.06/4)^(4 * 6)
Simplifying the equation:
$35,000 = P(1 + 0.015)^24
Dividing both sides by (1 + 0.015)^24:
$35,000 / (1 + 0.015)^24 = P
Calculating (1 + 0.015)^24:
(1.015)^24 = 1.435842 string
Dividing $35,000 by 1.435842:
$35,000 / 1.435842 = $24,384.89
Therefore, the company should invest approximately $24,384.89 to total $35,000 in 6 years, given an annual interest rate of 6% compounded quarterly.
To find the amount that should be invested to total $35,000 in 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($35,000)
P = the principal investment (unknown)
r = the annual interest rate (6% or 0.06)
n = the number of times interest is compounded per year (quarterly, so 4)
t = the number of years (6)
Rearranging the formula to solve for P:
P = A / (1 + r/n)^(nt)
Now we can plug in the given values:
P = $35,000 / (1 + 0.06/4)^(4*6)
Calculating inside the parentheses:
P = $35,000 / (1 + 0.015)^(24)
Simplifying further:
P = $35,000 / (1.015)^(24)
Using a calculator, we can compute the value inside the parentheses:
(1.015)^(24) ≈ 1.432
Now we can find the final amount:
P ≈ $35,000 / 1.432
P ≈ $24,399.44
The company should invest approximately $24,399.44 to reach the goal of $35,000 in 6 years.
x(1.015)^24 = 35000
x = 24484.04