Question

You decide to begin saving towards the purchase of a new car in 5 years. If you put $1,000
at the end of each of the next 5 years in a savings account paying 6 percent
compounded annually, how much will you accumulate after 5 years? What would be
the ending amount if the payments were made at the beginning of each year?

Answer 1

Present Value = $ 1,000 * 1/(1.06) ^ 1 + $ 1,000 * 1/(1.06) ^ 2 +$ 1,000 * 1/(1.06) ^ 3 +$ 1,000 * 1/(1.06) ^ 4+$ 1,000 * 1/(1.06) ^ 5

= $ 4,212.36

Future Value = Present Value * ( 1+ Rate of interest ) ^ Time

=$ 4,212.36 * ( 1+6/100) ^ 5

= $ 5,637.087894

Hence the correct answer is $ 5,637.09

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Present Value of Annuity Due =Present Value * ( 1+ Rate of Interest )

= $ 4,212.36 * ( 1+6/100)

= $ 4,465.1016

Future Value = Present Value of Annuity Due * ( 1+ Rate of interest ) ^ Time

=$ 4,465.1016* ( 1+6/100) ^ 5

= $ 5,975.313168

Hence the correct answer is $ 5,975.31