Suppose that at the end of each of the next 50 years you will deposit $1000 in an account paying $10% interest annually. Assuming that the first deposit will occur immediately, how much money will be in the account at the end of the 50 years? Round your final answer to two decimals.
What if the first deposit will occur one year from now?
The amount in the account after 50 years if the first deposit occurs immediately
Annual Deposits (P) = $1,000 per year
Annual interest rate (r) = 10.00% per year
Number of years (n) = 50 Years
Future Value of an Annuity Due is calculated by using the following Formula
Future Value of an Annuity Due = (1 + r) x P x [{(1+ r) n - 1} / r]
= (1 + 0.10) x $1,000 x [{(1 + 0.10)50 – 1} / 0.10]
= 1.10 x $1,000 x [(117.3908529 – 1) / 0.10]
= 1.10 x $1,000 x [116.3908529 / 0.10]
= 1.10 x $1,000 x 1163.908529
= $1,280,299.38
The amount in the account after 50 years if the first deposit occurs one year from now
Annual Deposits (P) = $1,000 per year
Annual interest rate (r) = 10.00% per year
Number of years (n) = 50 Years
Future Value of an Ordinary annuity is calculated by using the following Formula
Future Value of an Ordinary annuity = P x [{(1+ r) n - 1} / r]
= $1,000 x [{(1 + 0.10)50 – 1} / 0.10]
= $1,000 x [(117.3908529 – 1) / 0.10]
= $1,000 x [116.3908529 / 0.10]
= $1,000 x 1163.908529
= $1,163,908.53
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