Question

For the cash flow, interest rate and compounding frequency given below, what value of Q will make the inflows and outflows equivalent?

Compounding/y	NPERY	365
APR (nom/y)	NOMINAL	18.00%
Year	Cash Flow
0	($25,000)
1	-15*Q
2	+30*Q
3	$0
4	+12*Q
5	-14*Q
6	-2*Q
7	+6*Q
8	$0
9	-15*Q
10	-5*Q

Group of answer choices

$4,327

$8,347

$14,101

$22,891

Answer 1

Given rate = 18% compounded daily

converting it to Effective annual rate using formula

EAR = (1 + APR/n)^n - 1 = (1 + 0.18/365)^365 - 1 = 19.72%

now equating PV of the cash flow = 0, we get

-25000 -15Q/1.1972 +30Q/1.1972^2 + 12Q/1.1972^4 - 14Q/1.1972^5 - 2Q/1.1972^6 + 6Q/1.1972^7 -15Q/1.1972^9 -5Q/1.1972^10 = 0

So, 25000 = -12.53Q +20.93Q +5.84Q - 5.69Q -0.68Q + 1.70Q -2.97Q -0.83Q

So we get, Q = $4327

So option A is correct.