You are set to receive an annual payment of $11,400 per year for the next 20 years. Assume the interest rate is 6.3 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?

The payments are worth $8040.77 more if they are received at the beginning of the year rather than the end of the year.

Explanation:

The payments are in the form of an annuity as the amount of the payment is constant, is paid after equal intervals of time and is paid for a finite/limited time period. If the payments are received at the beginning of the year, we can classify the annuity as annuity due. On the other hand, if the payments are received at the end of the year, we can classify the annuity as annuity ordinary.

The formulas for the present value of annuity due and ordinary are attached.

We will calculate the PV of both annuity due and annuity ordinary and deduct the PV of annuity ordinary from the PV of annuity due to calculate how much more are the payments worth if they are received at the beginning of the year.

PV of annuity due = 11400 * [ (1 - (1+0.063)^-20) / 0.063 ] * (1+0.063)

PV of annuity due = $135672.0632 rounded off to $135672.06

PV of annuity ordinary = 11400 * [ (1 - (1+0.063)^-20) / 0.063 ]

PV of annuity ordinary = $127631.2919 rounded off to $127631.29

Difference = 135672.0632  -  127631.2919

Difference = $8040.771346 rounded off to $8040.77

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