Question

For what effective annual interest rate will an uniform cash flow of $1000 per year for 10 years be equivalent to a present amount of 8,982.6?

		0.5%
		1.0%
		2.0%
		3.0%
		4.0%

Answer 1

Answer is (c) " 2% "

According to question:-

PV = 8982.6

Per year cashflow = $1000

n = 10 years

So putting values in formula we have:-

PV = {R [ 1 - ( 1 + i )^-n ]} / i

8982.6 = [1000 { 1 - ( 1 + i )^-10 } ] / i

8982.6 / 1000 = { 1 - ( 1 + i )^-10 } / i

8.9826 = { 1 - ( 1 + i )^-10 } / i

So we have to find auch interest rate that we get PV = 8.9826

We can use hit and trial method to put values and check our answes. We will check for 0.5%, 1% and so on.

We see that at i=2% = 0.02 we get our equation satisfied

-----> { 1 - ( 1 + 0.02 )^-10 } / 0.02

-----> { 1 - ( 1.02 )^-10 } / 0.02 = 8.9826

Hence the interest rate required per annum is 2%.

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