present value. please help me with this?

Question

what is the present value of $10,000 you will receive in 5 years with an expected rate of interest of 8%, if discounted a) quarterly and b) continuously

a)
.08/12 = .0066

5 years = 60 months

PV = 10,000(1.0066/4)^4*60

b)
PV = 10,000 * e^(.08 * 5)

are those correct? thanks in advance to anyone helping me with this.

60 months = 6 years? I don't get that.

Answer 1

8% annually = 2% quarterly, so
a) PV = 10000/(1.02)^20 = $6,729.71

b) PV = 10000/e^(.08*5) = $6,703.20

You need to divide for PV. Multiplying gives the accumulated value, e.g., a bank CD. As we're dealing with quarterly compounding, we don't need the fact that 5 years = 60 months. If we were dealing with monthly compounding then the interest rate = .08/12 = .006667, and the formula would be
10000/(1.006667)^60

Answer 2

a) Present value of $10,000 @ 8% per annum discounted quarterly for 5 years:
= (1 / [1 + {0.08 / 4}]^[5 * 4]) * $10,000
= (1 / [1 + 0.02]^20) * $10,000
= (1 / [1.02]^20) * $10,000
= (1 / 1.485947395978350) * $10,000
= 0.672971333108057 * $10,000
= $6,729.71

b) Present value of $10,000 @ 8% per annum discounted monthly for 5 years:
= (1 / [1 + {0.08 / 12}]^[5 * 12]) * $10,000
= (1 / [1 + 0.006666666666667]^60) * $10,000
= (1 / [1.006666666666667]^60) * $10,000
= (1 / 1.489845708301610) * $10,000
= 0.671210444429163 * $10,000
= $6,712.10

Answer 3

PV = FV / (1 + i)^n

If interest is 8% per year, then it is 2% per quarter. And, there are 20 quarters in 5 years, so:

PV = 10,000 / (1 + 0.02) ^ 20
PV = 10,000 / 1.02^20
PV = 10,000 / 1.485947
PV = $6729.71

Answer 4

b is your proper answer60 mths =6 yrs