# Sum / Annuities question

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1. May 23, 2009

### Imperil

Find the final value of a plan in which payments of $800 are made every 6 months for 3 years, earning 10% interest compounded semi-annually. The first payment is made in 6 months. My Answer: R = 800, n = 6 , i = 5% A = R[(1-i)^n - 1] / i A = 800(1.05^6 - 1) / 0.05 A =$5441.53

So I calculated the annuity but I am thrown off by the last sentence. Since the first payment is made in 6 months does this mean that n should really be 5 because he is missing the first 6 months of the year? Or is 6 correct since it is semi-annual for 3 years? I'm just a little tripped up on the wording and started thinking that I am incorrect assuming n = 6 due to the final sentence.

Thanks

Last edited: May 23, 2009
2. May 23, 2009

### danago

I would say n=6, because he is payed in 6 months time and then again in 6 months after that i.e. twice in the current year. This continues for another two years, for a total of 6 payments.

3. May 23, 2009

### Imperil

Great thanks so much. That is what I originally thought but then started to second guess myself.