Question

Solve for the unknown quantity in Parts (a) through (d) that makes the equivalent value of cash outflows equal to the equivalent value of the cash inflow, a. If F-$9,500, G $570, and N-6, then i-? b. If F . $9,500, G-$570, and i-6% per period, then Ne ? C. If G:$900, N: 12, and i. 12% per penod, ten F ? d. Nf Fs $7,700, N#6, and 12% per period, then G z?

Answer 1

A. Given, F = $ 9,500 , G = $ 570, N = 6 years

The cash flow can be written as follows

G(P/G,i%,6) (F/P,i%,6)= F

$\large G \frac{(1+i)^n-in-1}{i^2(1+i)^n}(1+i)^n= F$

$\large 570 \frac{(1+i)^n-in-1}{i^2(1+i)^n}(1+i)^n= 9500$

$\large \frac{(1+i)^n-in-1}{i^2}= 16.66$

When i= 10%

(A/G,10%,6) = 17.51

It is greater than the required value. Let us assume i= 5%

(A/G,5%,6) = 16.03

The value lies in between 5 to 10 per cent thus we can calculate it using linear interpolation technique as follows

i=5 +(10-5)*(16.66-16.03)/(17.51-16.03)

Interest rate = 5 +5*0.63/1.48 = 7.13%

Required interest rate is 7.13%(Approximately).

B. F = $ 9500, G= $ 570, i=6%

G(P/G,6%,n)(F/P,6%,n) = F

(P/G,6%,N)(F/P,6%,N) = 16.67

(A/G,6%,N) = 16.67

Now, assume n = 6 years

(A/G,6%,6) = 1.419*11.459 = 16.26

Number of years = 6 years.

C. G = $ 900, i=12%, n = 12

F = G(F/G,i%,n)

F =900(P/G,12%,12)(F/P,12%,12)

F = 900*25.952*3.896

F = $ 90,998.09

D. F = $ 7700, N = 6, i = 12%, G= ?

F = G(F/G,i%,n)

F = G(F/P,i%,n)(P/G,i%,n)

$ 7,700 = G*(F/P,12%,12)(P/G,12%,12)

$7,700 = G*3.896*25.952

G * 101.1089 = $ 7,700

G = $ 76.16

Please contact if having any query. Will be obliged for your generous support thank you.