Question

In: Finance

Samantha wants to set up a fund which will provide in perpetuity a scholarship of $2,600...

Samantha wants to set up a fund which will provide in perpetuity a scholarship of $2,600

to a deserving student at the end of each year with the first payment being made one year

from today . Find the amount Betty should deposit today into the fund to provide for this

scholarship if the interest rate is 3.8% compounded quarterly.

Solutions

Expert Solution

$ 67,453.73

Step-1:Calculation of equivalent annual interest rate
Equivalent annual interest rate = ((1+(i/n))^n)-1
= ((1+(3.80%/4))^4)-1
= 3.85%
Where,
i = Nominal rate of interest = 3.80%
n = Number of times compounded in a year = 4
Step-2:Calculation of amount to be deposited today
Amount to be deposited today = Annual cash flow / Equivalent annual interest rate
= 2,600.00 / 3.85%
= 67,453.73

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