Solution:
Cash Flow(F )= $ 50,000
Rate = 10 %
Discounted Cash Flow of amount $50,000 (D)=
![F * ((1)/(1+(10)/(100)))^1+ F * ((1)/(1+(10)/(100)))^2+F * ((1)/(1+(10)/(100)))^3+F * ((1)/(1+(10)/(100)))^4+F * ((1)/(1+(10)/(100)))^5+..........\\\\= F * (10)/(11) + F * [(10)/(11)]^2+ F [* (10)/(11)]^3+..................................+ F [* (10)/(11)]^(20)](https://img.qammunity.org/2020/formulas/mathematics/high-school/9okyfltq29h6zyw822a56tdhidqxduxjfm.png)
As, this is a geometric Progression.
Formula for Sum of n terms of geometric Progression having common ratio r,

For, r < 1 and
for , r>1

![S_(20)=50,000 *(1 * ( [(11)/(10)]^(20)-1))/((11)/(10)-1)\\\\ S_(20)=50,000 * (6.7274-1)/(1.1-1)\\\\ S_(20)=50,000 * 57.27=2863500](https://img.qammunity.org/2020/formulas/mathematics/high-school/rleqqx4mxdpfkz5tb509ujo9e1l0a6z9kk.png)
If cash flow(K) = $ 25,000
Then at the rate of 10 % ,
Value after 20 years is given by:
Discounted Cash Flow of amount $25,000 (D)=
![K * ((1)/(1+(10)/(100)))^1+ K * ((1)/(1+(10)/(100)))^2+K * ((1)/(1+(10)/(100)))^3+K * ((1)/(1+(10)/(100)))^4+K * ((1)/(1+(10)/(100)))^5+..........\\\\ =K * (10)/(11) + K * [(10)/(11)]^2+ K [* (10)/(11)]^3+..................................+ K [* (10)/(11)]^(20)](https://img.qammunity.org/2020/formulas/mathematics/high-school/w6b8w5ox1ibjastjhhfr3i9c0bdwbyxnm2.png)
for , r>1, formula for sum of n terms of geometric series

![K_(20)=25,000 *(1 * ( [(11)/(10)]^(20)-1))/((11)/(10)-1)\\\\ K_(20)=25,000 * (6.7274-1)/(1.1-1)\\\\ K_(20)=25,000 * 57.27=1431750](https://img.qammunity.org/2020/formulas/mathematics/high-school/1u8wucg1fzhbf0rcyet0bv5j35m97fqrm8.png)