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Rudiy27
2 months ago
10

An investment pays you $30,000 at the end of this year, and $15,000 at the end of each of the four following years. What is the

present value (PV) of this investment, given that the interest rate is 5% per year
Business
1 answer:
Nady [3.6K]2 months ago
8 0

Answer:

The present value of the cash flow, discounted at a 5% annual rate, is $76,815.65.

Explanation:

First, we calculate the present value of a $15,000 annuity over 4 years:

C \times \frac{1-(1+r)^{-time} }{rate} = PV\\

C 15,000.00

Time 4

Rate 0.05

15000 \times \frac{1-(1+0.05)^{-4} }{0.05} = PV\\

PV $53,189.2576

Next, we discount two additional years as a lump sum, corresponding to two years following the investment:

\frac{Maturity}{(1 + rate)^{time} } = PV  

Maturity  53,189.26

Time  2.00

Rate  0.05000

\frac{53189.2575624354}{(1 + 0.05)^{2} } = PV  

PV   48,244.2245

Adding them results in the present value:

48,244.22 + 28,571.43 =  76,815.65  

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