Question

You want to buy a car for cash 5 years from now. The car price at that time will be 20000 dollars. To this end you want to make an annuity deposit each year so that you accumulate the required amount. Interest rate is 6%. How much do you have to deposit each year if (i) deposits are made at the end of each year (ii) deposits are made at the beginning of each year.

Answer 1

The deposit to be made at the end of each year

Future Value = $20,000

Annual Interest Rate (r) = 6% per year

Number of years (n) = 5 Years

Annual Deposits (P) = ?

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

$20,000 = P x [{(1 + 0.06)⁵ - 1} / 0.06]

$20,000 = P x [(1.3382256 – 1) / 0.06]

$20,000 = P x [0.3382256 / 0.06]

$20,000 = P x 5.6370930

P = $20,000 / 5.6370930

P = $3,547.93 per year

The deposit to be made at the beginning of each year.

Future Value = $20,000

Annual Interest Rate (r) = 6% per year

Number of years (n) = 5 Years

Annual Deposits (P) = ?

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

$20,000 = (1 + 0.06) x P x [{(1 + 0.06)⁵ - 1} / 0.06]

$20,000 = 1.06 x P x [(1.3382256 – 1) / 0.06]

$20,000 = 1.06 x P x [0.3382256 / 0.06]

$20,000 = 1.06 x P x 5.6370930

$20,000 = P x 5.9753185

P = $20,000 / 5.9753185

P = $3,347.10 per year