Question

An annuity makes payments of 2400 at the beginning of every 6 years over 54 years at an effective annual interest rate of 4 % . Find the present value of this annuity.

Possible Answers

8125

8711

9807

10,069

11,325

Answer 1

- Periodic annuity at the beginning of every 6 years over 54 years = $2400

Effective Annual Interest rate(EAR) = 4%

First, we will Calculate Effective 6-year Interest rate from EAR:-

Effective 6-year Interest rate = (1+EAR)^6 - 1

Effective 6-year Interest rate = (1+0.04)^6 - 1

Effective 6-year Interest rate = 1.265319 - 1

Effective 6-year Interest rate = 26.5319%

Now, Calculating the Present value of annuity using annuity due formula:-

Where, C= Periodic Payments = $2400

r = Periodic Interest rate = 26.5319%

n= no of Annuity payments = 54 years/6 years = 9

Present Value = $10069

Option 4

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