Question

1) An investment will pay $205,000 at the end of next year for an investment of $183,000 at the start of the year. If the market interest rate is 8% over the same period, should this investment be made?

2) Suppose you receive $100 at the end of each year for the next three years. a. If the interest rate is 8%, what is the present value of these cash flows? Compute the PV of this annuity both as the sum of PV of each cash flow and using the annuity formula.

Answer 1

1) Investment period = 1 year

future value (FV) = 205000

Presend value (PV) = 183000

% returns on investment = FV / PV - 1 = 205000/183000 = 12.02%

Market interest rate = 8%

Therefore investment should be made as investment returns are more than market returns

2) Annual annuity (A) = $100

no of annuities (n) = 3

Interst rate (i) = 8%

PV of cashflows:

year	cashflow	Present value factor @ 8%	Present Value
1	100	0.9259	92.59
2	100	0.8573	85.73
3	100	0.7938	79.38
Present Value of annuities			257.71

PV of annuities = A [(1-(1+i)^-n)/i] = 100 [(1-(1+0.08)^-3) / 0.08] = 100 [(1-0.79383) / 0.08]

PV of annuities = 100 x 2.5771 = $ 257.71

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