A wealthy singer has decided to endow her favorite hospital by establishing fund
ID: 2811276 • Letter: A
Question
A wealthy singer has decided to endow her favorite hospital by establishing funds for an endowment which would provide the hospital with $2,000,000 per year for medical research into perpetuity. The singer will give the endowment upon her 45th with the first payment on that birthday. She plans to accumulate the endowment by making annual equal deposits into an account from her 20th birthday until her 44th birthday. The rate of interest is expected to be 5 percent in all future periods. How much must the singer deposit each year to accumulate to the required amount?
A)$838,098.29
B)$ 798,188.85
C)$898,836.03
D)$856,034.31
E)$965,472.88
Explanation / Answer
Answer:
Value of corpus on 45th birthday = Yearly contribution ($2,000,000) / Interest Rate (5%)
Value of corpus on 45th birthday = $40,000,000
Given, yearly contribution to the corpus will start at singer's 20th birthday and last payment will be on 44th birthday.
Future value of yearly contribution = Value of corpus on 45th birthday ($40,000,000)
Future value of yearly contribution = Future value of annuity [ P * {(1+R)N - 1}/R ]
Future value of yearly contribution = P * {(1+5%)25 - 1}/5% i.e. P * 159.7
$40,000,000 = Periodic Payments * 47.7271
Periodic Payments = $838,098.29