SOLUTION: suppose u start saving today for a $45000 down payment that you plan to make on a house in 5 years. Assume that you make no deposits into the account after the initial deposit. For

Question 257741: suppose u start saving today for a $45000 down payment that you plan to make on a house in 5 years. Assume that you make no deposits into the account after the initial deposit. For the account described below, how much would you have to deposit now to reach for $45000 goal in 5 years.
an account with daily compounding and an APR of 4%

Found 2 solutions by rfer, Theo:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
P=A/(1+r/n)^nt
P=45000/(1+.04/365)^365*5
P=45000/(1.0001)^1825
P=45000/1.2
P=$37,500
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
daily compounding with annual interest rate of 4%.

formula is f = p * (1+r)^n

f = future value = 45000

p is what you're trying to find.

I believe daily compounding assumes 30 days each month totaling 360 days each year for financial purposes.

If you're not happy with this you can adjust to whatever days in the year you wish to have.

It won't make much of a difference either way.

r = 4% / 100% = .04 / 360 = .000111111

number of years is multiplied by 360 to get number of days.

you get 360 * 5 = 1800

n = number of time periods = 1800 days.

formula becomes:

45000 = p * (1.00011111)^1800

this becomes:

45000 = p * 1221389186

solve for p to get:

p = 45000 / 1.221389186 = 36843.29329

you would have to invest $36,843.29 today to have $45,000 in 5 years at 4% per year compounded daily.

--------------------------------------

following information is interesting to know but not necessary to solve your problem.

that was solved above the dashed line.

additional interesting information:

this figure is very close to what you would get with continuous compounding.

with continuous compounding, the formula would be:

f = p * e^(r*t)

e is the scientific constant of 2.718281828...

r = .04
t = 5 years

formula becomes:

45000 = p * e^(.04*5)

this becomes:

45000 = p * 1.221402758

solve for p to get:

p = 45000 / 1.221402758 = 36842.88389.

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