Question

You wish to have $10,000 in 20 years (t=20). Based on the current interest rate, you know if you deposit $9,000 today (t=0), you can achieve exactly that goal. Alternatively, you could deposit $______ 5 years from today to also reach that goal.

Answer 1

Calculation of interest rate:

Desired sum in 20 years = $10,000
Amount deposited today = $9,000

Amount deposited * (1 + Interest rate)^20 = Desired sum
$9,000 * (1 + Interest rate)^20 = $10,000
(1 + Interest rate)^20 = 1.11111
1 + Interest rate = 1.0053
Interest rate = 0.0053 or 0.53%

Calculation of deposit in 5 years:

Desired sum in 15 years = $10,000
Interest rate = 0.53%

Amount deposited * (1 + Interest rate)^15 = Desired sum
Amount deposited * (1 + 0.0053)^15 = $10,000
Amount deposited * 1.0053^15 = $10,000
Amount deposited * 1.08252 = $10,000
Amount deposited = $9,238

Alternatively, you could deposit $9,238 5 years from today to also reach that goal.