Question

he interest rate is 9% per year compounded semi annually. You account for your company's profits on a weekly basis. What is the effective rate to be used in using the time value of money equations to find the present or future value of an annuity? (Hint: CP and PP, 4 weeks in a month, 30 days in month, 26 weeks in 6 months, 52 weeks in a year)(Note: no units, the answer should be in decimals such that 10% is actually 0.1000, use 4 decimal points, threshold is 0.0001)

Answer 1

We assume the rate be x% weekly.

If $100 is deposited at the beginning of the year, the amount at the end of the year = 100 * (1+x/100)^52

Also, the amount will be the same as 100* (1+9/200)^2

So,100 * (1+x/100)^52 = 100* (1+9/200)^2

or (1+x/100)^52 = (1+9/200)^2

Solving for x, we get x = 0.16944

So the rate of interest is 0.16944% per week. = 0.16944*52% per year = 8.81% per year compounded weekly

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