SOLUTION: How much must be deposited today into the following account in order to have $ 30 comma 000 in 5  years for a down payment on a​ house? Assume no additional deposits are made

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Question 1206664: How much must be deposited today into the following account in order to have $ 30 comma 000 in 5  years for a down payment on a​ house? Assume no additional deposits are made.
An account with monthly compounding and an APR of 5​%
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
nominal interest rate per year = 5%.
you want to have 30,000 in 5 years.
how much do you have to deposit today.

this can be done by formula easy enough.
formula is f = p * (1 + r) ^ n that is solved for p as shown below.

start with f = p * (1 + r) ^ n
divide both sides of the formula by (1 + r) ^ n to get:
p = f / ((1 + r) ^ n)

f is the future value
p is the present value
r is the interest rate per time period (in decimal form, not % form)
n is the number of time periods.

in this problem, the timer periods are in months.
the interest rate per year is divided by 12 to get the interest rate per month.

the number of years are multiplied by 12 to get the number of months.

you can also use a calculator like the one at https://arachnoid.com/finance/

inputs to the calculator are:

present value = 0
future value = -30000
number of time periods = 5 years * 12 = 60 months.
interest rate per time period = 5% / 12 = .416666667% per month
payments per time period = 0

note that the calculator uses the % form of the interest rate.

click on present value and the calculator tells you that the present value is equal to 23376.16.

here's what the results look like in that calculator.



if you do it by formula, then the formula is p = f / ((1 + r) ^ n).

f = 30000
p = what you want to find
(1 + r) = (1 + .05/12)
n = 5 * 12 = 60

note that the formula uses the decimal form of the interest rate.

formula becomes p = 30000 / ((1 + .05/12) ^ 60) = 23376.16171 which rounds to 23376.16.

either way, you get the same answer.