19. 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?
A. $422.10
B. $432.60
C. $424.11
D. $426
V = Vo(1+r)^n.
Vo = $420.
r = 0.03/12 = 0.0025/mo.
n = 1Comp/mo. * 2mo. = 2 compounding periods.
V = ?.
To calculate the future value of money in your savings account after two months, we need to use the formula for compound interest:
Future Value = Present Value * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Time)
Given:
Present Value = $420
Interest Rate = 3% = 0.03 (as a decimal)
Number of Compounding Periods = 12 (compounded monthly)
Time = 2 months
Let's substitute these values into the formula:
Future Value = $420 * (1 + (0.03 / 12))^(12 * 2)
Future Value = $420 * (1 + 0.0025)^(24)
Future Value = $420 * (1.0025)^24
Future Value ≈ $420 * 1.061678
Future Value ≈ $446.59
Therefore, the future value of money in your savings account after two months is approximately $446.59.
None of the given answer options match exactly, but option C, $424.11, is the closest.