Question

Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years

Answer 1

The present value will be calculated as follows:

The interest for the 10 years:

$\text{Simple interest} = 10000\times10\times \dfrac{12}{100}= 12000$

Therefore, the amount will be:

$\text{Amount}=10000+12000=22000$

after 20yrs another payment will be received value of principal is 10000*2 = 20000

The interest will therefore, be:

$\text{Simple interest}=20000×20×\dfrac{12}{100}​=48,000$

$\text{Amount}=48,000+20,000=68,000$

Present value will therefore be:

$\text{Present value}=22000\times \dfrac{1}{(1+0.12)^{10}}+68000\times \dfrac{1}{(1+0.12)^{20}}$

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$\text{Present value}=14,132.75$