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Mike wants to donate $1,000,000 to establish a fund to provide an annual scholarship in perpetuity
Mike wants to donate $1,000,000 to establish a fund to provide an annual scholarship in perpetuity. The fund will earn an interest rate of j4=2.63% p.a. effective and the first scholarship will be first awarded 2.5 years after the date of the donation.
What is the amount of the annual scholarship (rounded to two decimal places)?
a) $27625.71
b) $28359.46
c) $26560.52
d) $27344.33
.
Expert Solution
Computation of the amount of annual scholarship:-
First we will calculate the value of fund donated by MIke at the end of year 1.5:-
Future Value = PV*(1+r)^n
Here,
Rate = 2.63%/4 = 0.6575%
n = 1.5 * 4 = 6 periods
FV = $1,000,000*(1+06575%)^6
= $1,000,000*1.0401
= $1,040,104.17
EAR = (!+rate/n)^n-1
= (1+2.63%/4)^4-1
= 1.0266 - 1
= 2.66%
Present value = Annual amount / Rate
$1,040,104.17 = Annual amount / 2.66%
Annual amount = $1,040,104.17 * 2.66%
= $27,625.71
Hence, the correct option is a) $27,625.71
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