Utilizing the compound interest formula:
The annual compound interest equation, including principal amount, is:
A = P (1 + r/n)ⁿˣ
Here:
A = future value = $95000
P = principal investment amount =?
r = annual interest rate = 0.06
n = frequency of compounding per year = 2
x = duration in years for investment = 0.5
95,000 = P (1 + 0.06/2)¹
95,000 = P (1 + 0.03)
95,000 = P (1.03)
P = 95,000 ÷ 1.03
P = 95,000 ÷ 1.03
P = 92,233.01
Total compounded interest = 92,233.01 - 95,000
Total compounded interest = -2,766.99
Answer:
Dow Jones Industrial Average on May 30, 2017:
As stated on valueline.com, on May 30, 2017, the Dow Jones Industrial Average concluded at 21029.47, reflecting a decrease of 50.81.
Closing index = 21029.47
minus the decline = 50.81
Opening index = 21080.28
This indicates that the opening figure was 21080.28.
Explanation:
The Dow Jones Industrial Average tracks the stock performance of 30 significant companies listed on U.S. stock exchanges. This is classified as a stock price index, alongside the S&P 500 and NASDAQ.
The opening index reflects the average price at the start of the trading day before any trades occurred. Throughout the trading period, prices likely fluctuated with various movements. By the trading day's conclusion, the closing price recorded was 21029.47, with a downward change of 50.81.
From this closing index data, one can deduce that the opening price exceeded the closing price by 50.81 or approximately 51 basis points.
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The formula for calculating the present value of an ordinary annuity is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
With the present value set at 300000
PMT is the amount for monthly payments?
R is the interest rate at 0.059
K indicates monthly compounding, which is 12 as payments are made monthly
N represents the time period of 30 years
To derive the formula for PMT
PMT=pv÷ [(1-(1+r/k)^(-kn))÷(r/k)]
PMT=300,000÷((1−(1+0.059÷12)^(
−12×30))÷(0.059÷12))
=1,779.41
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