Answer:The total amount in fund at the beginning of [tex]5^{th}[/tex] year = $10000 +$19,963.55 = $29,963.55
Explanation:
Initial amount to begin the fund = $10,000
Now , given ;
Church collects another $5,000 per year for the next 5 years at an interest rate of 8%.
Therefore we'll evaluate the Present value of these $5000 for the next 5 years.
PV = [tex]\frac{1}{(1+i)^{n}}\times 5000[/tex]
where ;
i = interest rate
n = time period
∴ Net Present Value = [tex]\left [ \frac{1}{(1+0.8)^{1}}+\frac{1}{(1+0.8)^{2}}+\frac{1}{(1+0.8)^{3}}+\frac{1}{(1+0.8)^{4}}+\frac{1}{(1+0.8)^{5}} \right ]\times 5000[/tex]
On evaluating the above equation;
Net Present Value = 5000×(0.926 + 0.857 + 0.794 + 0.735 + 0.681)
Net Present Value = $19,963.55
Now,
The total amount in fund at the beginning of [tex]5^{th}[/tex] year = $10000 +$19,963.55 = $29,963.55
