The present value of the money in your savings account is $420, and you're receiving 3% annual interest compounded monthly. What is the future value in two months?
Pt = Po (r + 1)^n.
Pt = Principal @ time t(2 mo.).
Po = Initial investment(420).
r = APR / 12 = 3% / 12 = 0.25 % = 0.0025 = rate / mo.
n = 12 comp. / yr * (1/6) yr = 2 comp
in 2 mo.
Pt = 420 (1.0025)^2 = 422.10.
To find the future value of money in your savings account after two months, you can use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate / Number of Compounding Periods) ^ (Number of Compounding Periods * Number of Years)
In this case, the present value is $420, the interest rate is 3% (or 0.03), and the money is compounded monthly, so the number of compounding periods per year is 12. The number of years is 2/12, which represents two months out of a year.
Let's calculate the future value:
Future Value = $420 * (1 + 0.03 / 12) ^ (12 * 2/12)
Future Value = $420 * (1 + 0.0025) ^ 2
Future Value = $420 * (1.0025) ^ 2
Future Value = $420 * 1.00500625
Future Value ≈ $422.10
So, the future value of the money in your savings account in two months, with the given interest rate and compounding frequency, would be approximately $422.10.