Question

Find the value of P for which the inflows will equal the outflows. Find the effective rate first.

Rate 8% p y c d
Year Outflows Inflows
0 -P
1 -2P
2 -4P
3 -8P
4 -16P
5 $24,000
6 $30,000
7 $36,000
8 $42,000
9 $48,000
10 $54,000

Answer 1

The answer is "p= $5,246".

Explanation:

Using formula:

Present value of
`(in-flow)/(out-flow)` = cash-flow
`*` present value of discounting factor(rate %, time period)

`\to -p-(2p)/(1.08)-(4p)/(1.08^2)- (8p)/(1.08^3)-(16p)/(1.08^4) =(24000)/(1.08^5)+ (30000)/(1.08^6)+ (36000)/(1.08^7) + (42000)/(1.08^8)+ (48000)/(1.08^9)+ (24000)/(1.08^(10))\\\\`

`\to -p[1+(2)/(1.08)+(4)/(1.08^2)+ (8)/(1.08^3)+(16)/(1.08^4)] = 127960.43169\\\\\to -p[24.3923427] = 127960.43169\\\\\to -p = (127960.43169)/(24.3923427)\\\\\to p= 5245.93\\\\\to p= 5246`