Question

Your neighbor Bob has two annuities. The first annuity will pay him $10,000 per month for the next 10 years. The second annuity will pay him $15,000 per month for the following 10 years (years 11 through 20). Assuming a discount rate of 6%, what is the present value of the annuities?

Answer 1

Answer:

$1,643,344.308

Explanation:

These are Ordinary annuities because if it is not mentioned that the payments are made at the beginning of the year which is the case for Annuity Due.

You can use a financial calculator to find the Present value of these two ordinary annuities.

PV of Annuity 1 from (yr1-yr10)

Recurring payment; PMT = 10,000

Total duration ; N = 10 *12 = 120 months

Monthly interest rate in this case ; I/Y = 6%/12 = 0.50%

Future value ; FV = 0 (use 0 if annuity variable is not given )

then CPT PV= $900,734.533

PV of Annuity 1 from (yr11-yr20)

This will happen in 2 steps sice it is a forward-starting annuity;

Recurring payment; PMT = 15,000

Total duration ; N = 10 *12 = 120 months

Monthly interest rate in this case ; I/Y = 6%/12 = 0.50%

Future value ; FV = 0 (use 0 if annuity variable is not given )

then CPT PV( at t=10)= $1,351,101.80

Next find the PV of $1,351,101.80  at t=0;

$1,351,101.80 /(1.005^120) = $742,609.7754

Next, find the sum of these two PVs to find the answer;

=$900,734.533 + $742,609.7754

PV = $1,643,344.308