An educational foundation has been o ered a donation that will fund a scholarship
for two years. The rst scholarship award of $18,000 will be paid one year from today. The second
scholarship award of $19,000 will be paid two years from today. The foundation has opened an
account earning interest at an annual percentage rate of 4%, compounded continuously, into which
the donor will immediately deposit sucient funds to cover both awards. How much does the donor
need to deposit? (Rounded to two decimal places.)
for two years. The rst scholarship award of $18,000 will be paid one year from today. The second
scholarship award of $19,000 will be paid two years from today. The foundation has opened an
account earning interest at an annual percentage rate of 4%, compounded continuously, into which
the donor will immediately deposit sucient funds to cover both awards. How much does the donor
need to deposit? (Rounded to two decimal places.)
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Think of making two deposits today: one to cover the $18,000 paid in 1 year, and the other to cover the $19,000 paid in 2 years.
The continuously compounded interest formula is A = Pe^(rt), so P = Ae^(-rt).
The deposit needed in order to cover the $18,000 in 1 year is $18,000e^(-0.04*1).
The deposit needed in order to cover the $19,000 in 2 years is $19,000e^(-0.04*2).
So the total deposit needed today is
$18,000e^(-0.04*1) + $19,000e^(-0.04*2), or approximately $34,833.42 .
Lord bless you today!
The continuously compounded interest formula is A = Pe^(rt), so P = Ae^(-rt).
The deposit needed in order to cover the $18,000 in 1 year is $18,000e^(-0.04*1).
The deposit needed in order to cover the $19,000 in 2 years is $19,000e^(-0.04*2).
So the total deposit needed today is
$18,000e^(-0.04*1) + $19,000e^(-0.04*2), or approximately $34,833.42 .
Lord bless you today!
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We use a negative rate since we must work backwards; we need to find how much to deposit to achieve a certain balance later. Using a positive rate wouldn't make sense, because that would result in deposits greater instead of less than the balance that is needed later.
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a) $ 17294.21
b) $ 17539.21
ADD $34,833.42 ANSWER
b) $ 17539.21
ADD $34,833.42 ANSWER