Question

The cash flows have a present value of 0. Compute the value of n, assuming a 10% interest rate compounded annually?Year Cash Flow Amount 0 0 1 1 2 1 --- 1 n-2 1 n-1 1 n 1 n -35.95

Answer 1

The value of n is 16

Step-by-step explanation:

Note: Organized table is as attached

Present Worth of Cash-inflow = Present worth of Cash Outflow

$1 [(1+i)^n -1 / i(1+i)^N] = $35.95[1 / (1+i)^n]

$1 [ (1+0.10)^n - 1/ 0.10(1+0.10)^n] = $35.95[ 1 / (1+0.10)^n]

$1 [ (1.1)^n - 1 / 0.10(1.1)^n] = $35.95 [1/(1.1)^n]

Let (1.1)n be x

[x-1/x] = [$35.95 * 0.10 / $1] * [1/x]

[x-1/x] = 3.595[1/x]

x - 1 = 3.595

x = 3.595 + 1

x = 4.595

(1.1)^n = 4.595

Take log on both side

nlog (1.1) = log (4.595)

n(0.041392685) = 0.662285515

n = 0.662285515 / 0.041392685

n = 16.000062

n = 16

Thus, the value of n is 16