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an annuity is an arrangement where a sum invested is paid out (including interest) over a number of years. How much must I invest now at 5.48% p.a. in order to be paid $2000 at the end of each year from year 1 to year 13? (no funds remain after the year 13 payment.

total paid = 2000 x 13 = 26000

r = 0.0548

Sn = a (r^n - 1) / (r-1) 26000 = a (1.0548^13 - 1)/(1.0548 - 1) a = 1423.61

Invest = 13 x a = 13 x 1423.61 = 18506.92

BUT answer = 18255.80 ???

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  • $\begingroup$ why answer is different from given answer of 18255.80?? $\endgroup$ – sekling Nov 13 '14 at 17:15
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Hint: You have to calculate the present value.

$PV=r\cdot \frac{q^n-1}{q-1}\cdot \frac{1}{q^n}=2000\cdot \frac{1.0548^{13}-1}{0.0548}\cdot \frac{1}{1.0548^{13}}$

It is asked how much you have to invest NOW ...

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  • $\begingroup$ Present Value of an Ordinary Annuity Formula PV = P [1-(1+r)^-n]/r PV = 2000 [1-(1+0.0548)^-13]/0.0548 PV = $18255.80 THANKS for coaching $\endgroup$ – sekling Nov 14 '14 at 2:37

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