a company will need $30,000 IN 7 YEARS FOR AN ADDTION. TO MEET THIS GOAL THE COMPANY DEPOSITS MONEY IN AN ACCOUNT TODAY THAT PAYS 7% ANNUAL INTREST COMPONDED QUARTERLY. TO FIND THE AMOUNT THAT SHOULD BE INVESTED TO $30,000 IN 7 YEARS.
HOW MUCH SHOULD THE COMPANY INVEST?
P = Po*(1+r)^n
r = (7%/4)/100% = 0.0175 = Quarterly % rate expressed as a decimal.
n = 4 Comp./yr. * 7yrs. = 28 Compounding
periods.
P = Po*(1.0175)^28 = 30,000
Po = 30,000/(1.0175)^28 = $18,456.85 =
Initial deposit.
To find out how much the company should invest today to reach $30,000 in 7 years at an annual interest rate of 7% compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($30,000 in this case)
P = the initial principal or amount to be invested today
r = the annual interest rate (7% in this case, which is written as 0.07)
n = the number of times interest is compounded per year (4 times, since it is compounded quarterly)
t = the number of years (7 years in this case)
Let's solve for P:
$30,000 = P(1 + 0.07/4)^(4*7)
Simplifying the equation:
30,000 = P(1.0175)^(28)
To find the value of P, we need to divide both sides of the equation by (1.0175)^(28):
P = $30,000 / (1.0175)^(28)
Using a calculator to evaluate (1.0175)^(28) approximately equals 1.2202, we can substitute that value into the formula:
P = $30,000 / 1.2202
P ≈ $24,593.59
Therefore, the company should invest approximately $24,593.59 today to reach $30,000 in 7 years with an interest rate of 7% compounded quarterly.