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[SOWHAT0819]

24.Find the weekly yield (in %) for an investment that has a interest rate of 9.76% compounded quarterly

 

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To find the weekly yield for an investment with an interest rate of 9.76% compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (9.76% = 0.0976)
n = the number of times interest is compounded per year (quarterly = 4)
t = the number of years the money is invested for (1 year = 52 weeks)

Assuming we invest $1, we can substitute the values into the formula:

A = 1(1 + 0.0976/4)^(4*1)
A = 1(1 + 0.0244)^4
A = 1(1.0244)^4
A = 1(1.10080286)
A = 1.10080286

To find the weekly yield, we need to calculate the growth factor:

Growth Factor = A^(1/t) = 1.10080286^(1/52)

The weekly yield is the growth factor minus 1, multiplied by 100% to E×ρréšš it as a percentage:

Weekly Yield = (Growth Factor - 1) * 100%

Let's calculate it:

Weekly Yield = (1.10080286^(1/52) - 1) * 100%
Weekly Yield ≈ (1.00185565 - 1) * 100%
Weekly Yield ≈ 0.00185565 * 100%
Weekly Yield ≈ 0.185565%

Therefore, the weekly yield for an investment with an interest rate of 9.76% compounded quarterly is approximately 0.185565%.