Question

1. Your church has decided that one of its missions will be to provide assistance to those members that demonstrate a need for assistance to attend local community colleges. The board decided to set-up a trust fund that will be available in 5 years. One member puts up $10,000 to begin the fund. The church also collects another $5,000 per year for the next 5 years. How much will the fund have beginning in 5 years? Assume an interest rate of 8%.

Answer 1

Answer:The total amount in fund at the beginning of $5^{th}$ 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 = $\frac{1}{(1+i)^{n}}\times 5000$

where ;

i = interest rate

n = time period

∴ Net Present Value = $\left [ \frac{1}{(1+0.8)^{1}}+\frac{1}{(1+0.8)^{2}}+\frac{1}{(1+0.8)^{3}}+\frac{1}{(1+0.8)^{4}}+\frac{1}{(1+0.8)^{5}} \right ]\times 5000$

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 $5^{th}$ year = $10000 +$19,963.55 = $29,963.55