Question

1. What is the present value of $10,000 to be received in 6 years? Your required rate of return is 8% per year.

2. If you invest $1,000 a year for 20 years at 7% annual interest, how much will you have at the end of the 20^th year?
3. If you buy a 5 year, 3% CD for $2,000. How much is it worth at maturity?

4. How much would you be willing to pay today for an investment that pays $900 per year at the end of the next 10 years? Your required rate of return is 6% per year.

Answer 1

1)

PV = FV / (1+r)ⁿ
FV = cash flow in future period
r = the periodic rate of return or interest
n = number of periods

FV = $10000

n = 6 years

r = 8%

Present Value = 10000/(1+8%)^6 = $6301.69

2)

FV = (PMT [((1 + r)n - 1) / r])(1 + r)

FV = Future value of the annuity stream to be paid in the future
PMT = Amount of each annuity payment
r = Periodic rate of return or interest
n = Number of periods

FV = (1000[((1+7%)20-1)/7%])(1+7%) = $40995.49

3)

FV = PV * (1+r)ⁿ

PV = Present Value

FV = cash flow in future period
r = the periodic rate of return or interest
n = number of periods

FV =2000 * (1 + 3%)^5 = $2318.54

4)

PV = PMT [(1 - (1 / (1 + r)n)) / r]

PV = Present value of the annuity stream to be paid in the future

PMT = The amount of each annuity payment

r = The interest rate

n = The number of periods over which payments are to be made

PV = 900 [(1 - (1 / (1 + 6%)10)) / 6%] = $6624.07