Question

(c) Calculate the periodic payment of an annuity due of N70,000, payable annually for 3 years at 15% compounded annually.

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Answer to a math question (c) Calculate the periodic payment of an annuity due of N70,000, payable annually for 3 years at 15% compounded annually.

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Hank
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97 Answers
To calculate the periodic payment of an annuity due, we can use the formula for the present value of an annuity due:

PV = Pmt \times \frac{{1 - (1 + r)^{-n}}} {r}

where:
PV = Present value of the annuity
Pmt = Periodic payment of the annuity due
r = Interest rate per period
n = Number of periods

Given:
PV = N70,000
r = 15\% = 0.15
n = 3

Substitute the given values into the formula:

70,000 = Pmt \times \frac{{1 - (1 + 0.15)^{-3}}} {0.15}

70,000 = Pmt \times \frac{{1 - (1.15)^{-3}}} {0.15}

70,000 = Pmt \times \frac{{1 - 0.6575}} {0.15}

70,000 = Pmt \times \frac{{0.3425}} {0.15}

70,000 = Pmt \times 2.2833

Pmt = \frac{{70,000}} {2.2833}

Pmt \approx 30,641.64

Therefore, the periodic payment of the annuity due is approximately $30,641.64.

\boxed{Pmt \approx 30,641.64}

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