A passbook savings account has a rate of 8%. Find the effective annual yield if the interest is compounded quarterly.
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Don't you need to know the amount in the account first?
yes i do not
To find the effective annual yield of a passbook savings account with quarterly compounding, we need to use the formula for compound interest:
A = P(1+r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested for
In this case, the annual interest rate is 8% which can be written as 0.08 in decimal form. The interest is compounded quarterly, so n = 4.
Using the formula, the effective annual yield can be calculated as follows:
A = P(1+r/n)^(n*t)
= 1(1+0.08/4)^(4*1)
= (1+0.02)^4
= (1.02)^4
≈ 1.0824
To convert this to a percentage, subtract 1 and multiply by 100:
Effective annual yield = (1.0824 - 1) * 100
≈ 8.24%
Therefore, the effective annual yield for a passbook savings account with an annual interest rate of 8% and quarterly compounding is approximately 8.24%.
To find the effective annual yield of a passbook savings account with compounded interest, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the accumulated amount (the final amount with interest)
P = the principal amount (the initial amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
r = 8% = 0.08 (as a decimal)
n = 4 (compounded quarterly)
To find the effective annual yield, we want to know what the interest rate would be if it were compounded annually. So, we need to solve for r:
0.08 = r/4
Multiply both sides of the equation by 4:
0.32 = r
Now that we have the annual interest rate, we can calculate the effective annual yield:
A = P(1 + r/n)^(nt)
A = P(1 + 0.32/4)^(4 * t)
Since it is not specified how many years (t) we are considering, we can assume it to be 1 year:
A = P(1 + 0.32/4)^(4 * 1)
A = P(1 + 0.08)^4
Simplifying the formula:
A = P(1.08)^4
Therefore, the effective annual yield for a passbook savings account with an interest rate of 8% compounded quarterly is approximately 4.858% (using the formula A = P(1.08)^4 and converting it to a percentage).