You want to have $85,000 college fund in 15 years. HOw much will you have to deposit now under the scenario below. Assume that you make no deposits into the account after the initial deposit

An APR of 4% compounded daily.
You should invest?

P = Po(1+r)^n = $85,000

r = (4%/365)/100% = 0.000109589 = Daily
% rate expressed as a decimal and based
on 365 days per year.

n = 365Comp/yr. * 15yrs. = 5475 Compounding periods.

P = Po(1.000109589)^5475 = 85000
Po = 85000/(1.000109589)^5475 = $46650.53

To calculate the initial deposit required to achieve a college fund of $85,000 in 15 years with an APR of 4% compounded daily, we can use the formula for compound interest:

A = P(1+r/n)^(nt)

Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (4% or 0.04 in decimal form)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years

By rearranging the formula, we can solve for P:

P = A / (1+r/n)^(nt)

Substituting the given values:
A = $85,000
r = 0.04
n = 365
t = 15

P = $85,000 / (1+0.04/365)^(365*15)

Calculating this equation, the initial deposit required to achieve a college fund of $85,000 in 15 years with an APR of 4% compounded daily is approximately $41,671.11.

To calculate the amount you need to deposit now to have $85,000 in 15 years with a 4% APR compounded daily, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment ($85,000)
P = the principal amount (the amount to be deposited now)
r = annual interest rate (4% or 0.04)
n = number of times interest is compounded per year (365 for daily compounding)
t = number of years (15)

Now, let's plug in the values into the formula:

$85,000 = P(1 + 0.04/365)^(365*15)

To solve for P, we need to isolate it on one side of the equation. Divide both sides of the equation by (1 + 0.04/365)^(365*15):

P = $85,000 / (1 + 0.04/365)^(365*15)

Using a calculator to evaluate the right-hand side of the equation, we find:

P ≈ $85,000 / (1.000109589)^5475

P ≈ $85,000 / 1.668625203

Therefore, you should deposit approximately $50,928.74 now to have a $85,000 college fund in 15 years with an APR of 4% compounded daily.

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