Question

3-part question. Five years from now you would like to have $25,000
for a down payment on a home. Assuming you could earn 9% interest,
how much money would you need to invest today as a lump sum to meet
your goal? How much money would you have to invest at the end of
each year to meet your goal? How much would you need if you
invested the payments at the beginning of each year with the first
payment deposited today?

Answer #1

first part;

present value of single amount = future value / (1+r)^n

here,

future value = $25,000

r=9%

=>0.09.

n=5 years.

=>25,000/(1.09)^5

=>$16,248.28.

second part;

future value of annuity = P [(1+r)^n-1]/r

here,

future value = 25,000

P is to be found out.

r=0.09.

n=5.

25,000= P [(1.09)^5-1]/0.09

=>25,000 =P*5.98471056.

=>P = $4,177.31.

yearly deposit = $4,177.31.

third part;

future value of annuity immediated = P + P[(1+r)^(n-1)]/r

25,000 = P + P[(1.09)^(4)-1]/0.09.

=>25,000 = P + 4.573129 P

=>25,000 = 5.573129P

=.P = $4,485.81.

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