Question

a) What is the present value of $40 earned 2-years from now if compounding was semi-annual...

a) What is the present value of $40 earned 2-years from now if compounding was semi-annual and the interest rate is annually 3%?

b) A “black box” just paid $20, which is expected to grow by 3% when the interest rate is 7% forever, what is the present value of this “black box”?

c) What is the future value of an annuity due with a $15 cash flow, 4% annual interest with quarterly compounding three-years from now?

d) If the monthly interest rate is 0.5%, then what is the effective annual rate? What is the stated annual rate?

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Answer #1

1: PV = FV/(1+r)^n

= 40/(1+3%/2)^(2*2)

=$37.69

2: Present value of the black box = expected value/(k-g)

= 20*103%/(7%-3%)

=$515

3: FV = (1+r)*P*((1+r)^n-1)/r

= (1+ 4%/4)*15*((1+4%/4)^(4*3)-1)/(4%/4)

=$192.14

4: EAR = (1+APR/n)^n -1

= (1+ 0.5%)^12 -1

=6.17%

Stated rate = 0.5%*12 = 6%

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