Stuart estimates that he will need $25000 to set up a small business in 7years.How much must stuart invest at 12% interest compound quarterly to achieve goal?
PV = 25000(1.03)^-28
= $10,926.92
i = .12/4 = .03
n = 7(4) = 28
Thank you reiny:)
Stuart estimates that he will need $25000 to set up a small business in 7years.
Answer A=$10,926.92
Answer B=$14,073.08
To calculate how much Stuart must invest at a 12% interest rate compounded quarterly to achieve his goal of $25000 in 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future value (the goal amount of $25000 in this case)
P = the principal amount (the amount Stuart needs to invest)
r = the annual interest rate (12% in this case, expressed as a decimal: 0.12)
n = the number of times the interest is compounded per year (quarterly in this case, so n = 4)
t = the number of years (7 in this case)
Now, let's plug in the values and solve for P:
25000 = P(1 + 0.12/4)^(4*7)
First, simplify the exponents:
25000 = P(1 + 0.03)^(28)
Next, add 1 to 0.03 and raise it to the power of 28:
25000 = P(1.03)^(28)
Now, divide both sides by (1.03)^(28) to isolate P:
P = 25000 / (1.03)^(28)
Using a calculator, we can evaluate (1.03)^(28) to be approximately 2.0798473:
P = 25000 / 2.0798473
P ≈ $12010.83
Therefore, Stuart must invest approximately $12010.83 at a 12% interest rate compounded quarterly to achieve his goal of $25000 in 7 years.