Question

1. In finance, we study the future value of money to determine how much cash flows will grow over a given period. If you invest $400 at the end of the next seven (7) years, (a) and your opportunity cost is 6 percent compounded annually, what will your investment be worth after you make the last $400 payment? (b) If the payments are made at the beginning of each year what will be the ending amount?

Answer 1

The value ending amount if the payments are made at the end of each year (Future Value of Ordinary Annuity)

Annual Payments = $400 per year

Interest Rate (r) = 6% per year

Number of Years = 7 Years

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

= $400 x [{(1 + 0.06)⁷ – 1} / 0.06]

= $400 x [(1.503630 – 1) / 0.06]

= $400 x [0.503630 / 0.06]

= $400 x 8.393837

= $3,357.54

“The value ending amount would be $3,357.54”

The value ending amount if the payments are made at the beginning of each year (Future Value of an Annuity Due)

Annual Payments = $400 per year

Interest Rate (r) = 6% per year

Number of Years = 7 Years

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

= (1 + 0.06) x $400 x [{(1 + 0.06)⁷ – 1} / 0.06]

= 1.06 x $400 x [(1.503630 – 1) / 0.06]

= 1.06 x $400 x [0.503630 / 0.06]

= 1.06 x $400 x 8.393837

= $3,558.99

“The value ending amount would be $3,558.99”