you deposit $750 in an account earning 10.3% interest compounded monthly. Find the interest earned in 6 months.
To find the interest earned in 6 months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan
P = the principal investment amount (the initial deposit)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years
In this case, the principal amount (P) is $750, the annual interest rate (r) is 10.3% or 0.103 (in decimal form), the interest is compounded monthly (n = 12), and the time period (t) is 6 months or 0.5 years.
Plugging in the values, we get:
A = 750(1 + 0.103/12)^(12*0.5)
Now we can calculate the interest earned (A - P):
Interest earned = A - P
Let's calculate it step by step:
Step 1: Calculate the value inside the parentheses
(1 + 0.103/12) = 1.008583333
Step 2: Calculate the exponent
12 * 0.5 = 6
Step 3: Calculate the future value (A)
A = 750 * 1.008583333^(6)
A ≈ 787.07
Step 4: Calculate the interest earned
Interest earned = A - P
Interest earned ≈ 787.07 - 750
Interest earned ≈ 37.07
Therefore, the interest earned in 6 months is approximately $37.07.