Question

What is the present value (PV) of an investment that pays $90,000 every year for four years if the interest rate is 9% APR, compounded quarterly?

Answer 1

- Periodic annual annuity for 4 years = $90,000

Interest rate = 9% compounded quarterly

First, Calculating Effective ANnual rate(EAR) of compounded quarterly:-

Where,

r = Interest rate = 9%

m = no of times compounding in a year = 4 (compounded Quarterly)

EAR = 9.3083%

Now, Calculating the Present Value of annual annuity:-

Where, C= Periodic Payments = $90,000

r = Periodic Interest rate = 9.3083%

n= no of periods = 4

Present value = $289,612.55