Question

# You wish to have \$10,000 in 20 years (t=20). Based on the current interest rate, you...

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.

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.

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