Investment A: $5,000 invested for 7 years compounded semiannually at 9%.
Investment B: $ 6,000 invested for 5 years compounded quarterly at 4.1%.
Find each total for each investment and determine which investment results are greater.
A: amount = 5000(1.045)^14 = ....
b: amount = 6000(1.01025)^20 = ....
A(t) = P (1 + r/n)^nt
P = 5000, t = 7, r = .09, n = 2
A(7) = 5000 (1 + .09/2)^2(7)
A(7) = 5000 (1 + 0.045)^14
A(7) = 5000 (1.045)^14
A(7) = $9259.72 interest
5000 + 9259.72 = 14259.72
A(t) = P (1 + r/n)^nt
P = 6000, t = 5, r = .0410, n = 4
A(7) = 6000 (1 + .0410/4)^4(5)
A(7) = 6000 (1 + 0.01025)^20
A(7) = 6000 (1.01025)^20
A(7) = $7357.47 interest
6000 + 7357.47 = 13357.47
check my math
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30000(e.055.5)
To find the total for each investment, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
For Investment A:
P = $5,000
r = 9% = 0.09 (as a decimal)
n = 2 (compounded semiannually)
t = 7 years
Plugging these values into the formula, we get:
A = 5000(1 + 0.09/2)^(2*7)
A = 5000(1 + 0.045)^(14)
A = 5000(1.045)^(14)
A ≈ $8,793.58
For Investment B:
P = $6,000
r = 4.1% = 0.041 (as a decimal)
n = 4 (compounded quarterly)
t = 5 years
Plugging these values into the formula, we get:
A = 6000(1 + 0.041/4)^(4*5)
A = 6000(1 + 0.01025)^(20)
A = 6000(1.01025)^(20)
A ≈ $7,271.64
Therefore, the total for Investment A is approximately $8,793.58, and the total for Investment B is approximately $7,271.64.
To compare the results, we can see that Investment A resulted in a higher total amount compared to Investment B.