# Engineering Economics Question

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Posted 24 August 2010 - 04:08 PM

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

### #2 cdcengineer

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Posted 24 August 2010 - 04:32 PM

((((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.

### #3 eedave

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Posted 24 August 2010 - 04:38 PM

QUOTE (roadrunner @ Aug 24 2010, 11:08 AM) <{POST_SNAPBACK}>
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 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)

Intern

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Posted 24 August 2010 - 04:41 PM

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!!

Edited by roadrunner, 24 August 2010 - 04:43 PM.

### #5 BamaBino

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Posted 25 August 2010 - 09:35 PM

QUOTE (eedave @ Aug 24 2010, 11:38 AM) <{POST_SNAPBACK}>
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)

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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