Question

2. Jim Stewart promised to pay his son $200 semiannually for 6 years. If Jim can invest his money at 8% in an ordinary annuity, how much must Jim invest today to be able to pay his son $200 semiannually for 6 years?

Answer 1

The amount is computed as shown below:

Present value is computed as follows:

= Future value / (1 + r)ⁿ

r is computed as follows:

= 8% / 2 (Since the amount is semi annual hence divided by 2)

= 4% or 0.04

n is computed as follows:

= 6 x 2 (Since the amount is semi annual hence multiplied by 2)

= 12

So, the amount will be:

= $ 200 / 1.04¹ + $ 200 / 1.04² + $ 200 / 1.04³ + $ 200 / 1.04⁴ + $ 200 / 1.04⁵ + $ 200 / 1.04⁶ + $ 200 / 1.04⁷ + $ 200 / 1.04⁸ + $ 200 / 1.04⁹ + $ 200 / 1.04¹⁰ + $ 200 / 1.04¹¹ + $ 200 / 1.04¹²

= $ 1,877.01 Approximately

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