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.

True or False: Assume you wish to have a certain amount saved
four years from now, and you plan to make a one-time deposit today
in an interest-bearing account earning interest of 10%.
As the compounding frequency of interest decreases, the amount
you need to invest today in order to achieve your goal will
increase.
Select one:
True
False

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