You plan to take a break from work life after 16 years in the job. To...

You plan to take a break from work life after 16 years in the job. To provide for that break, you initiate a savings program of $1000 per year in an investment yielding 8%. What will the value of the fund be and the end of the 16th year (ordinary annuity)? What is the future value if the payment is deposited at the beginning of each year (annuity due)?

Solutions

Expert Solution

The value of the fund be and the end of the 16th year (ordinary annuity)

Annual Payments = $1,000 per year

Interest Rate (r) = 8%

Number of Years = 16 Years

Future Value of Ordinary Annuity = P x [{(1+ r) ⁿ - 1} / r ]

= $1,000 x [{(1 + 0.08)¹⁶ – 1} / 0.08]

= $1,000 x [(3.42594 – 1) / 0.08]

= $1,000 x [2.42594 / 0.08]

= $1,000 x 30.32428

= $30,324.28

“The value of the fund be and the end of the 16th year = $30,324.28”

The future value if the payment is deposited at the beginning of each year (annuity due)

Annual Payments = $1,000 per year

Interest Rate (r) = 8%

Number of Years = 16 Years

Future Value of Ordinary Annuity = (1 + r) x P x [{(1+ r) ⁿ - 1} / r ]

= (1 + 0.08) x $1,000 x [{(1 + 0.08)¹⁶ – 1} / 0.08]

= 1.08 x $1,000 x [(3.42594 – 1) / 0.08]

= 1.08 x $1,000 x [2.42594 / 0.08]

= 1.08 x $1,000 x 30.32428

= $32,750.23

“The future value if the payment is deposited at the beginning of each year = $32,750.23”

jeff jeffy answered 1 year ago

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