Question

How much money should Shelby invest today in a fund that earns interest at 4.02% compounded quarterly, if she wants to receive $5,750 at the end of every 6 months for the next 4 years?
Round to the nearest cent

Answer 1

PV = ??

Interest Rate = 4.02% p.a. Compounded Quarterly

Payment to be recieved = $5750

Frequency of Reciept = 6 Months

Total Duration = 4 Years

Interest Rate (Semiannual) = (1 + Yearly Rate / Number of Quarters)^{(Number of Quarters in a half year)} - 1

Interest Rate (Semiannual) = (1 + 4.02% / 4)² - 1

Interest Rate (Semiannual) = 2.02%

Now for calculating Present value of future cashflows which we want to receive, we can use present value of annuity formula.

=

= (5750 / 2.02%) * (1 - 1 / (1 + 2.02%)⁸)

= $42085.05

Shelby need to invest $42085.05 today for receiving $5750 for 8 times at a gap of 6 months.