Question

Assume that you have found an investment fund that will earn you $500 at the end of each month for 10 years. However, you will receive your first payment 2 years from now. The investment yield is 6% compounded monthly. How much do you need to deposit today?

Answer 1

The amount is computed as follows:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 6% / 12 (Since interest is compounded monthly, hence divided by 12)

= 0.5% or 0.005

n will be as follows:

= 10 x 12 (Since interest is compounded monthly, hence multiplied by 12)

= 120

So, the amount will be as follows:

= $ 500 x [(1 - 1 / (1 + 0.005)¹²⁰ ) / 0.005 ]

= $ 500 x 90.07345333

= $ 45,036.72666

Now the above amount has been computed 2 years from now, so the present value of the same will be as follows:

= $ 45,036.72666 / (1 + 0.06 / 12)^{12 x 2}

= $ 45,036.72666 / 1.005²⁴

= $ 39,955.94 Approximately

Feel free to ask in case of any query relating to this question