Solve the following exercise by using the present value formula.
Mike Gioulis would like to have $33,000 in 4 years to pay off a balloon payment on his business mortgage. His money market account is paying 2.19% compounded daily.Disregarding leap years, how much money must Mike put in his account now to achieve his goal? Do not round intermediate calculations. Round to the nearest whole dollar.
2.19% compounded daily --- daily rate = .0219/365 = .00006 per day
number of days in 4 years = 1460
x(1.00006)^1460 = 33,000
x = 33000/(1.00006)^1460 = 30,232.28
Thank you!
To solve this exercise using the present value formula, we need to calculate the amount of money (present value) that Mike needs to put in his money market account now.
The present value formula is as follows:
Present Value = Future Value / (1 + interest rate)^(number of periods)
In this case, the Future Value is $33,000, the interest rate is 2.19% (expressed as a decimal, 0.0219), and the number of periods is 4 years.
Using the formula, we have:
Present Value = $33,000 / (1 + 0.0219)^(4)
We can now calculate the present value using a calculator or a spreadsheet. Here are the intermediate calculations:
(1 + 0.0219) = 1.0219
(1.0219)^4 = 1.088523533
Now, we can substitute these values back into the formula:
Present Value = $33,000 / 1.088523533
Calculating this:
Present Value = $30,336.08 (rounded to the nearest whole dollar)
Therefore, Mike must put approximately $30,336 into his money market account now to achieve his goal of $33,000 in 4 years, assuming an interest rate of 2.19% compounded daily.