Asked by math
The assistant to the president of an executive search firm starts a saving plan by depositing $95 at the beginning of each week into an account that earns an annual interest rate of 4.75% compounded weekly. Find the value (in dollars) of this investment after 7 years. (Round your answer to the nearest cent.)
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Answered by
GPT 3.5
To find the value of the investment after 7 years, we will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount ($95 deposited at the beginning of each week)
r = the annual interest rate (4.75% or 0.0475)
n = the number of times the interest is compounded per year (weekly compounding means n = 52)
t = the number of years (7 years)
First, we need to calculate the weekly interest rate:
Weekly interest rate = Annual interest rate / Number of compounding periods per year
Weekly interest rate = 0.0475 / 52 = 0.00091346154
Now we can plug in the values into the formula and calculate the future value of the investment:
A = 95(1 + 0.00091346154)^(52*7)
A = 95(1.00091346154)^364
A = 95 * 1.3723145363
A = 130.67
Therefore, the value of the investment after 7 years would be approximately $130.67.
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount ($95 deposited at the beginning of each week)
r = the annual interest rate (4.75% or 0.0475)
n = the number of times the interest is compounded per year (weekly compounding means n = 52)
t = the number of years (7 years)
First, we need to calculate the weekly interest rate:
Weekly interest rate = Annual interest rate / Number of compounding periods per year
Weekly interest rate = 0.0475 / 52 = 0.00091346154
Now we can plug in the values into the formula and calculate the future value of the investment:
A = 95(1 + 0.00091346154)^(52*7)
A = 95(1.00091346154)^364
A = 95 * 1.3723145363
A = 130.67
Therefore, the value of the investment after 7 years would be approximately $130.67.
Answered by
GPT 3.5
Apologies for the calculation error. Let's recalculate:
A = P(1 + r/n)^(nt)
A = 95(1 + 0.0475/52)^(52*7)
A = 95(1 + 0.00091346154)^364
A = 95(1.00091346154)^364
A = 95 * 2.036298
A = 193.85
After 7 years, the value of the investment would be approximately $193.85.
A = P(1 + r/n)^(nt)
A = 95(1 + 0.0475/52)^(52*7)
A = 95(1 + 0.00091346154)^364
A = 95(1.00091346154)^364
A = 95 * 2.036298
A = 193.85
After 7 years, the value of the investment would be approximately $193.85.
Answered by
GPT 3.5
Apologies for the mistake in my previous calculations. Let's recalculate the future value of the investment after 7 years.
Given:
P = $95 (deposited at the beginning of each week)
r = 4.75% = 0.0475 (annual interest rate)
n = 52 (number of times the interest is compounded per year)
t = 7 years
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Substitute the values:
A = 95(1 + 0.0475/52)^(52*7)
A = 95(1 + 0.00091346154)^364
A = 95 * 2.2381575
A = 213.02
Therefore, the value of the investment after 7 years should be approximately $213.02.
Given:
P = $95 (deposited at the beginning of each week)
r = 4.75% = 0.0475 (annual interest rate)
n = 52 (number of times the interest is compounded per year)
t = 7 years
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Substitute the values:
A = 95(1 + 0.0475/52)^(52*7)
A = 95(1 + 0.00091346154)^364
A = 95 * 2.2381575
A = 213.02
Therefore, the value of the investment after 7 years should be approximately $213.02.
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