# Engineering Economics Question



## roadrunner (Aug 24, 2010)

I don't understand this question.

Assume an effective interest rate of 15% per year compounded annually. An investment requires $1500 at the end of each year for the next 5 years plus a final investment of $3000 in 5 years. What is the equivalent lump sum investment now?

A. $6100

B. $6500

C. $8000

D. $8700

the answer is B?!?!?!?!?


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## cdcengineer (Aug 24, 2010)

((((6500*1.15)*1.15)*1.15)*1.15)*1.15 is most nearly equal to the following:

year 1 end 1500+year 2 end 1500=3000*1.15=3450

3450+year 3 end 1500=4950*1.15=5692.50

5692.5+year 4 end 1500=7192.50*1.15=8271.375

(8271.375+3000 lump sum at end)*1.15=12962.08

I know there is a formula for the 6500 @ 1.15 for 5 years, but I don't remember it.


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## eedave (Aug 24, 2010)

roadrunner said:


> I don't understand this question.
> Assume an effective interest rate of 15% per year compounded annually. An investment requires $1500 at the end of each year for the next 5 years plus a final investment of $3000 in 5 years. What is the equivalent lump sum investment now?
> 
> A. $6100
> ...


The effective interest rate is i=0.15 (given)

The future value of the annuity is A*((1+i)^n-1)/i ($10,113.57)

Add the future payment of $3000 giving a total investment of FV=$13,113.57 (in period 5)

The question asks for the lump sum investment today; the present value of Total Investment is FV/(1+i)^n ($6519.76)


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## roadrunner (Aug 24, 2010)

Well maybe I the question is misprinted or something because the solutions they provide do not match that.

I got $13,113 using F = A[ [(1+i)^n - 1] / i]

I did find a solution it says:

1500[ [(1+.15) - 1] / [(.15)(1+.15)] ] + (3000)(1+.15)^-5

= 5028.23 + 1491.53 = 6519.76

**NOTE eedave posted while i was typing and answered my question. Thx eedave!!


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## BamaBino (Aug 25, 2010)

eedave said:


> The effective interest rate is i=0.15 (given)
> The future value of the annuity is A*((1+i)^n-1)/i ($10,113.57)
> 
> Add the future payment of $3000 giving a total investment of FV=$13,113.57 (in period 5)
> ...


I converted both the annuity and the final payment directly to the Present Value.

Instead of determining the FV of both then converting the total to PV.

PV of 5 annuity of $1500 = $5028

PV of final $3000 = $1491

Total PV = $ 6520


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