Question

change if you endow it now, but it makes the first award to a student 10 years from today? In the first case, te amount you must donate today is S□ (Round to the nearest cent)

Answer 1

The first case is that of a perpetuity. The formula to calculate the present of a perpetuity is given as:

$PV=\frac{C}{r}$

Where

• C is the cash flow, starting one year from now
• r is the discount rate

Substituting the values,

$PV=\frac{5,000}{0.06}=83,333.33$

So, an amount of $83,333.33 needs to be endowed

---------------------------------------------------------------------------

In the second case, the perpetuity starts 10 years from now but the amount is endowed today. To solve this, simply discount the present value of annuity calculated above by 10 periods to get its value today. (Please note that the value of perpetuity does not change. It doesnt matter if it starts today of 10 years from now, its value is going to be the same. The only difference is that now, that value will be at period 10 and will have to be discounted to period 0)

The formula to calculate present value of a given future value is,

$PV=\frac{FV}{(1+r)^{n}}$

Where,

• FV is the future value
• r is the discount rate
• n is the period

So, substituting the given values

$PV=\frac{83,333.33}{(1+0.06)^{10}}=46,532.9$

So, in the second case $46,532 need to be endowed.