Paul bought $3,500 worth of government bonds that pay 3% interest compounded quarterly. If no money is deposited or withdrawn, how much will the bonds will be worth after 10 years?
Everything the bot does is correct until the last line, lol
....
$3,500 (1.0075)^40
= $4,719.22
To calculate the future value of the government bonds after 10 years, we need to use the compound interest formula:
FV = PV * (1 + r/n)^(n*t)
where:
FV = future value
PV = present value (initial investment)
r = annual interest rate (as a decimal)
n = number of compounding periods per year
t = number of years
Given that:
PV = $3,500
r = 3% = 0.03 (as a decimal)
n = 4 (quarterly compounding)
t = 10 years
Plugging these values into the formula, we have:
FV = $3,500 * (1 + 0.03/4)^(4*10)
Calculating inside the parentheses first:
FV = $3,500 * (1 + 0.0075)^(40)
Next, raise the value inside the parentheses to the power of 40:
FV = $3,500 * (1.0075)^(40)
Using a calculator or spreadsheet, we can find:
FV ≈ $4,604.56
Therefore, the bonds will be worth approximately $4,604.56 after 10 years.
To calculate the future value of the government bonds after 10 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 (in this case, $3,500)
r = annual interest rate (3% in this case)
n = number of times the interest is compounded per year (quarterly, so 4)
t = number of years (10 years in this case)
Substituting the given values into the formula, we have:
A = 3500(1 + 0.03/4)^(4*10)
Let's calculate this using basic algebraic simplification:
A = 3500(1 + 0.0075)^(40)
A = 3500(1.0075)^(40)
Now, we can calculate the future value of the bonds:
A = 3500 * (1.0075)^(40)
Using a calculator, compute 1.0075 raised to the power of 40, and multiply the result by 3500.
A ≈ $4,747.68
Therefore, the bonds will be worth approximately $4,747.68 after 10 years if no money is deposited or withdrawn.
To solve this problem, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
where:
A = the amount of money after t years
P = the principal (initial amount invested)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $3,500, r = 0.03 (3%), n = 4 (compounded quarterly), and t = 10 years. Therefore,
A = $3,500 (1 + 0.03/4)^(4*10)
= $3,500 (1.0075)^40
= $4,872.24
Therefore, the bonds will be worth approximately $4,872.24 after 10 years, if no money is deposited or withdrawn.