Question

A wealthy art collector has decided to endow her favorite art museum by establishing funds for an endowment which would provide the museum with $1,000,000 per year for acquisitions into perpetuity. The art collector will give the endowment upon her fiftieth birthday 10 years from today. She plans to accumulate the endowment by making annual end-of-year deposits into an account. The rate of interest is expected to be 6% in all future periods. How much must the art collector deposit each year to accumulate to the required amount?

A. $1,575,333.
B. $736,000.
C. $943,396.
D. $1,264,466.
E. $2,264,466

Answer 1

Answer:

Given:

Annuity = $1,000,000

Rate of interest = 6%

First, we'll equate present value of this endowment:

$Present \:Value = \frac{Annuity}{Rate}$

=$\frac{1000000}{0.06}$

= $16,666,666.67

We will further compute the required annual deposit:

$Annuity \:payment = \frac{rate(Present\: value)}{1- (1+r)^{n} }$

= $\frac{0.06(16666666)}{1- (1+0.06)^{10} }$

= $1,264,465.97

Therefore the correct option is (d.)