Find the present value of the annuity necessary to fund the withdrawal of $600 per month for 10 years, if the annuity earns 2% per year and if there is to be $10,000 to be left in the annuity at the end of the 10 years. (Assume end-of-period withdrawal and compounding at the same intervals as withdrawal. Round your answer to the nearest ten cents.)

Question

Find the present value of the annuity necessary to fund the withdrawal of $600 per month for 10 years, if the annuity earns 2% per year and if there is to be $10,000 to be left in the annuity at the end of the 10 years. (Assume end-of-period withdrawal and compounding at the same intervals as withdrawal. Round your answer to the nearest ten cents.)

Answer 1

i = .02/12 = .0016666667

n= 120

PV = 600[ 1 - 1.001666667^-120]/.00166667 + 10000(1.00166667)^-120
= .....

I got 73 396.55, let me know if you did not get that.

Answer 2

To find the present value of the annuity, we can use the formula for the present value of an ordinary annuity.

The formula is:

PV = PMT * [1 - (1 + r/n)^(-nt)] / (r/n)

Where PV is the present value of the annuity, PMT is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Given:
PMT = $600 per month
r = 2% per year (or 0.02)
n = 12 (since the compounding is done monthly)
t = 10 years

We need to calculate the present value (PV) that would allow for a $600 monthly withdrawal for 10 years while leaving $10,000 in the annuity at the end.

First, let's calculate the total number of withdrawals over the 10-year period:

Total number of withdrawals = number of years * number of compounding periods per year
Total number of withdrawals = 10 years * 12 months per year
Total number of withdrawals = 120

Next, let's calculate the present value of the annuity using the formula:

PV = $600 * [1 - (1 + 0.02/12)^(-12*10)] / (0.02/12)

Simplifying the formula:

PV = $600 * [1 - (1 + 0.00167)^(-120)] / (0.00167)

Using a calculator, calculate the value inside the brackets first:

(1 + 0.00167)^(-120) ≈ 0.72747

Now, substitute this value back into the formula:

PV = $600 * [1 - 0.72747] / (0.00167)

Calculate the value inside the square brackets:

[1 - 0.72747] ≈ 0.27253

Now, substitute this back into the formula:

PV = $600 * 0.27253 / (0.00167)

Finally, calculate the present value:

PV ≈ $98,127.84

Therefore, the present value of the annuity necessary to fund the withdrawal of $600 per month for 10 years, with an annual interest rate of 2% and leaving $10,000 in the annuity at the end, is approximately $98,127.84.