Answer to Question #119933 in Financial Math for Piya

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

When the cash flow is received at the beginning of the year, the cash flow is termed as ordinary annuity. The present value of ordinary annuity is computed using the following formula:

$\text{Present value of ordinary annuity}=\text{cashflow} \times \dfrac{1-(1+i)^{-n} }{i}$

$\text{Present value of ordinary annuity}=10,000 \times \dfrac{1-(1+0.12)^{-20} }{0.12}$

$\text{Present value of ordinary annuity}=\blue{74,694.44}$

On the other hand, when the cash flow is received at the end of the year, it is referred to as annuity due. The present value of an annuity due is computed using the formula below:

$\text{Present value of an annuity due}=\text{cashflow} \times \dfrac{1-(1+i)^{-n} }{i}\times (1+i)$

$\text{Present value of an annuity due}=10,000 \times \dfrac{1-(1+0.12)^{-20} }{0.12}\times (1+0.12)$

$\text{Present value of an annuity due}=\blue{83,657.77}$