Question

XYZ wants to establish a charitable foundation that will make annual donations to GMU forever. XYZ wants the foundation to make the first annual donation payment to GMU in 7 years from today, she wants that first donation payment to be $27,000, and she wants annual donations to GMU to increase by 1.6 percent per year forever. To fund the foundation, XYZ plans to make equal annual savings contributions to the foundation for 6 years. How much does XYZ need to contribute to the foundation each year for 6 years to have exactly enough in the foundation to meet her goal if she makes her first contribution to the foundation in one year from today, all savings contributions to the foundation are equal, and funds held by the foundation are expected to earn 8.1 percent per year? a. 558.805 (plus or minus 510) b. 556.481(plus or minus 510) c. 552.249 (plus or minus 510) d. 546.411 (plus or minus 510) e. None of the above is within 510 of the correct answer

Answer 1

XYZ wants to make annual donation forever starting from 7 year from today.

Annual donation which will be paid forever = $27000

This donation will grow after its 1 st payment (g)= 1.6%

Interest rate (r) = 8.1%

First, we will Calculate the Present value at year end 6 of Balance required to fund annual donation each year :-

PV = Donation/(r-g)

= $27,000/(0.081-0.016)

= $415,384.615

So, This Present value will be the Future value to calculate the annual contribution Required.

Calculation the annual contribution using Present value of Annuity formula:-

$Future Value= C*\frac{[(1+r)^{n}-1]}{r}$

Where, C= Periodic Payments

r = Periodic Interest rate =0.081

n= no of periods =6

Future Value = $415,384.615

$415,384.615= C*\frac{[(1+0.081)^{6}-1]}{0.081}$

$415,384.615= C*\frac{[1.59571072395-1]}{0.081}$

C = $ 56,480.69

So, The annual contribution Required each year for 6 years is $ 56,481

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Hence, option B