At a certain interest rate the present value of the following two payment patterns areequal: (i)$200 at the end of 5 years plus$500 at the end of 10 years. (ii)$400.94 atthe end of 5 years. At the same interest rate$100 invested now plus$120 invested atthe end of 5 years will accumulate to P at the end of 10 years. Calculate P.

P = $917.77

Explanation:

The computation of the P is shown below:

Let us assume i% be the annual interest rate

Now  

Present value of 1st Payment Pattern is

= $200 ÷ (1+i)^5 + $500/(1+i)^10

Present value of 2nd Payment Pattern is

= $400.94 ÷ (1+i)^5

Now equate these two above equations

PV of 1st Payment Pattern = PV of 2nd Payment Pattern

$200 ÷ (1+i)^5 + $500 ÷ (1+i)^10 = $400.94 ÷ (1+i)^5

$500 ÷ (1+i)^10 = $200.94 ÷ (1+i)^5

2.4883 = (1+i)^5

1+i = 1.20

i = 0.20

= 20.00%

Now  

P =  $100 × 1.20^10 + $120 × 1.20^5

P = $917.77

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