margaret Hillman invested $4,000 at 1.2% compounded quarterly for one year. find the futrue value and the interest earned for the year
FV=4000(1.02)
interest earned: .02*4000
i = .012/4 , (compounded quarterly)
= .003
n = 4
amount = 4000(1.003)^4 = 4048.22
interest earned = $48.22
To find the future value and the interest earned for the year, you can use the formula for compound interest:
Future Value (FV) = Principal (P) * (1 + (r/n))^(n*t)
where:
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
Here's how you can calculate it for Margaret Hillman's investment:
Given:
Principal (P) = $4,000
Annual interest rate (r) = 1.2% = 0.012 (in decimal form)
Compounding periods per year (n) = 4 (quarterly)
Number of years (t) = 1
Step 1: Calculate the future value (FV):
FV = $4,000 * (1 + (0.012/4))^(4*1)
FV = $4,000 * (1 + 0.003)^4
FV = $4,000 * (1.003)^4
FV = $4,000 * 1.0120488
FV = $4,048.20
The future value of the investment after one year is $4,048.20.
Step 2: Calculate the interest earned (I):
I = FV - P
I = $4,048.20 - $4,000
I = $48.20
The interest earned for the year is $48.20.
Therefore, the future value of the investment after one year is $4,048.20 and the interest earned is $48.20.
To find the future value and the interest earned, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Future value
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $4,000
r = 1.2% = 0.012 (converted to decimal form)
n = 4 (compounded quarterly)
t = 1 year
Now we can plug in these values to calculate the future value:
A = 4000(1 + 0.012/4)^(4*1)
A = 4000(1 + 0.003)^4
A = 4000(1.003)^4
A ≈ 4000(1.012048)
A ≈ $4,848.19
So, the future value of Margaret Hillman's investment after one year is approximately $4,848.19.
To determine the interest earned, we subtract the initial investment from the future value:
Interest earned = Future value - Principal amount
Interest earned = $4,848.19 - $4,000
Interest earned ≈ $848.19
Therefore, Margaret Hillman earned approximately $848.19 in interest for the year.