Would you prefer to receive an annuity due for $5,000 per year for 8 years or...

Would you prefer to receive an annuity due for $5,000 per year for 8 years or otherwise similar ordinary annuity? Interest rate is 7%. Explain numerically.

Solutions

Expert Solution

Information provided:

Yearly payment= $5,000

Time= 8 years

Interest rate= 7%

Annuity Due

Annuity due refers to annuity that occurs at the beginning of a period.

This is solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2^nd BGN 2^nd SET on the Texas BA II Plus calculator.

The future value of annuity due is solved using a financial calculator by inputting the below into the calculator

PMT= 5,000

N= 8

I/Y= 7

Press the CPT key and FV to calculate the future value of the annuity due.

The value obtained is $54,889.94.

Ordinary Annuity

Ordinary Annuity refers to an annuity that occurs at the end of the period.

The future value of an ordinary annuity can be calculated with the help of a financial calculator. The calculator by default is the END mode that is needed to calculate ordinary annuity values.

The future value of ordinary annuity is calculated by entering the below in the financial calculator:

PMT= 5,000

N= 8

I/Y= 7

Press the CPT key and FV to calculate the future value of the annuity due.

The value obtained is $51,299.02.

In the question, the future value of annuity due is $51,299.02 while the future value of ordinary annuity is $54,889.94. Since annuity due payments are made at the beginning of the period, annuity due has a higher value than an ordinary annuity. This is because the yearly payments earn interest for one additional period in annuity due.

I would therefore prefer annuity due since the future value is greater.

jeff jeffy answered 1 year ago

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