Each year, Eric invests $2500 at 8.2%/a compounded annually for 25 years.
a) Calculate the value of each of the first four investments at the end
of 25 years.
To calculate the value of each of the first four investments at the end of 25 years, 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
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, Eric is investing $2500 at an annual interest rate of 8.2% compounded annually for 25 years.
Let's calculate the value of each of the first four investments at the end of 25 years:
First investment:
P = $2500
r = 8.2% = 0.082 (as a decimal)
n = 1 (compounded annually)
t = 25 years
A1 = 2500(1 + 0.082/1)^(1*25)
A1 ≈ $10,628.32
Second investment:
P = $2500
r = 8.2% = 0.082 (as a decimal)
n = 1 (compounded annually)
t = 25 years
A2 = 2500(1 + 0.082/1)^(1*25)
A2 ≈ $10,628.32
Third investment:
P = $2500
r = 8.2% = 0.082 (as a decimal)
n = 1 (compounded annually)
t = 25 years
A3 = 2500(1 + 0.082/1)^(1*25)
A3 ≈ $10,628.32
Fourth investment:
P = $2500
r = 8.2% = 0.082 (as a decimal)
n = 1 (compounded annually)
t = 25 years
A4 = 2500(1 + 0.082/1)^(1*25)
A4 ≈ $10,628.32
Therefore, the value of each of the first four investments at the end of 25 years is approximately $10,628.32.
To calculate the value of each of the first four investments at the end of 25 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (the initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years the money is invested for
Given:
P = $2500
r = 8.2% (or 0.082 as a decimal)
n = 1 (compounded annually)
t = 25 years
Let's calculate the value of each of the first four investments one by one:
First investment:
A1 = 2500(1 + 0.082/1)^(1*25)
A1 = 2500(1 + 0.082)^(25)
A1 ≈ $10,790.25
Second investment:
A2 = 2500(1 + 0.082/1)^(1*25)
A2 = 2500(1 + 0.082)^(25)
A2 ≈ $23,498.86
Third investment:
A3 = 2500(1 + 0.082/1)^(1*25)
A3 = 2500(1 + 0.082)^(25)
A3 ≈ $40,438.45
Fourth investment:
A4 = 2500(1 + 0.082/1)^(1*25)
A4 = 2500(1 + 0.082)^(25)
A4 ≈ $69,658.10
Therefore, the value of each of the first four investments at the end of 25 years is approximately:
First investment: $10,790.25
Second investment: $23,498.86
Third investment: $40,438.45
Fourth investment: $69,658.10