To calculate the principal that must be deposited in a savings account to reach a certain amount after a certain number of years with a certain interest rate, we can use the formula:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the principal (initial amount), r is the annual interest rate, t is the number of years, and n is the number of times the interest is compounded per year.
In this case, we know that:
A = $10,000
r = 4.5%
t = 8 years
n = 12 (monthly compounding)
So we can set up the equation as:
$10,000 = P(1 + 0.045/12)^(12*8)
To solve for P, we can divide both sides by (1 + 0.045/12)^(12*8)
P = $10,000 / (1 + 0.045/12)^(12*8)
P = $5,964.35
So the principal that must be deposited in a 4.5% saving account compounded monthly to have a total of $10,000 after 8 years is $5,964.35
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Answer:
To calculate the principal that must be deposited in a savings account to reach a certain amount after a certain number of years with a certain interest rate, we can use the formula:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the principal (initial amount), r is the annual interest rate, t is the number of years, and n is the number of times the interest is compounded per year.
In this case, we know that:
A = $10,000
r = 4.5%
t = 8 years
n = 12 (monthly compounding)
So we can set up the equation as:
$10,000 = P(1 + 0.045/12)^(12*8)
To solve for P, we can divide both sides by (1 + 0.045/12)^(12*8)
P = $10,000 / (1 + 0.045/12)^(12*8)
P = $5,964.35
So the principal that must be deposited in a 4.5% saving account compounded monthly to have a total of $10,000 after 8 years is $5,964.35
Step-by-step explanation: