Mike Gioulis would like to have $25,000 in 4 years to pay off a balloon payment on his business mortgage. His money market account is paying 1.825% compounded daily. Disregarding leap years, how much money must Mike put in his account now to achieve his goal? Round to the nearest whole dollar.

well, I can do it using daily but I bet continuous compounding will give the same answer to the nearest dollar :)

anyway daily interest = .01825/365
= 5 * 10^-5
number of periods = 365 * 4 = 1460

1 + 5*10^-5 = 1.00005
1.00005^1460 = 1.07573 note this multiplier
1.07573 x = 25,000
x = 23,240
===============
now just for fun if continuous
a = p e^rt
a = p e^(5*10^-5*1460)
a = p e^ (.073)
a = p (1.07573)
LOL see !

26000/ 1.0757285738 =

24,170

23,240

Well, Mike definitely has a "balloon" situation on his hands! But fear not, I'm here to inflate the situation with a joke and help him out.

To calculate the amount Mike needs to put in his money market account, we can use the formula for compound interest:

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

Where:
A = the future value (the amount Mike needs in 4 years, $25,000)
P = the principal amount (the initial deposit)
r = the annual interest rate (1.825% or 0.01825)
n = the number of times that interest is compounded per year (since it's compounded daily, n = 365)
t = the number of years (4)

Now let's plug in the numbers and calculate:

$25,000 = P(1 + 0.01825/365)^(365*4)

With my brilliant math skills and a dash of clown magic, I've crunched the numbers and found out that Mike needs to put approximately $24,344 in his account now to achieve his goal.

Now that's a lot of money! But hey, every balloon has its price, right?

To calculate the amount of money Mike must put in his money market account now, 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 (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

Given:
Future value (A) = $25,000
Interest rate (r) = 1.825% = 0.01825 (as a decimal)
Compounding frequency (n) = 365 (compounded daily)
Time (t) = 4 years

We need to solve for the principal amount (P).

25,000 = P(1 + 0.01825/365)^(365*4)

25,000 = P(1 + 0.00005)^(1,460)

25,000 = P(1.00005)^1,460

25,000 / (1.00005)^1,460 = P

P ≈ $22,369.74

Therefore, Mike must put approximately $22,369.74 into his account now to achieve his goal of $25,000 in 4 years when the money market account is paying 1.825% compounded daily.

To calculate how much money Mike must put into his account now to achieve his goal, we need to use the future value formula for compound interest. The formula is:

Future Value = Present Value * (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods * Time)

In this case, the Present Value is what we need to find, the Interest Rate is 1.825%, the Number of Compounding Periods is the number of days in a year (365), and the Time is 4 years.

Using the formula, we can calculate the Present Value:

Future Value = Present Value * (1 + 0.01825 / 365)^(365 * 4)

To isolate the Present Value, divide both sides of the equation by the part in parenthesis:

Present Value = Future Value / (1 + 0.01825 / 365)^(365 * 4)

Now, let's substitute the given values into the equation:

Present Value = $25,000 / (1 + 0.01825 / 365)^(365 * 4)

Calculating the exponential part first:

(1 + 0.01825 / 365)^(365 * 4) = 1.01958485

Now, substitute back into the equation:

Present Value = $25,000 / 1.01958485

Calculating the Present Value:

Present Value = $25,000 / 1.01958485 ≈ $24,532.36

Therefore, Mike must put approximately $24,532 into his money market account now to achieve his goal of having $25,000 in 4 years, rounded to the nearest whole dollar.