Please help! How much should you put in the bank every month if you are earning 2.5% interest compounded monthly?

Question

 You need to save money to go on vacation at Disney World. You figure it will take about $10,000 to take you and your family on this vacation. You want this money in 4 years. How much should you put in the bank every month if you are earning 2.5% interest compounded monthly?

Answer 1

This is a Future Value Annuity Due Problem to determine the monthly deposit needed to save $10,000 in 4 years.

Present Value = $0

Future Value = $10,000

N (number of years) =4 years ( 4 X 12) =48 Months

I (Interest Rate) = 2.5% compounding monthly or 30% Annually (Very High Interest Rate)

Use Future Value of Annuity Due formula as follows:

P = PMT x (((1 + r) ^ n - 1) / r)

Where PMT = The Future Value

r= Interest Rate

n= Number of Periods

P= 10,000 X (((1+.025)^48-1)/.025 =$110.06 per month.

(1+.025)^48-1 = 2.27149; 2.27149/.025= 90.85958; $10,000/90.85958 =$110.06

You can double check by reversing course and determine the future value by using the following FV Formula:

$110.06 X ((1.025)^48-1)/.025) = $10,000