Question

You are set to receive an annual payment of $12,100 per year for the next 17 years. Assume the interest rate is 7 percent. How much more are the payments worth if they are received at the beginning of the year rather than the end of the year

Answer 1

The difference in value is worth $8,269 more in money.

Step-by-step explanation:

Case 1. Payments are made at the end of each year

So here, we will use the annuity formula for computing the present value of payments that we are receiving at the end of each year.

Here

Annual Cash flow is $12,100

Interest Rate "r" is 7%

And

Number of Payments "n" will be 17

Present Value = Cash flow * [1 - 1 / (1+r)^n] / r

By putting values, we have:

Present Value = $12,100 * [1 - 1 / (1 + 7%)^17] / 7%

Present Value = $12,100 * 9.763223

Present Value = $118,135

Now

Cash 2. Payments are arising at the start of each year

Just like the case above, we will use the annuity formula for computing the present value of payments that we are receiving at the start of each year. The first payment will be at worth the same because it is received in today's price.

So

Present Value = Cash flow + Cash flow * [1 - 1 / (1+r)^n] / r

So by putting values, that were used in case 1, we have:

Present Value = $12,100 + $12,100 * (1 - (1/1.07)^16) / 0.07

Present Value = $12,100 + $12,100 * 9.446649

Present Value = $126,404

Difference in Present Value = PV of Case 1 - PV of Case 2

= $126,404 - $118,135 = $8,269

The difference in value is worth $8,269 more in money.