a client invests 100 000 with an interest rate of 8% with quarterly compound what will the interest be after a year
100000 [1 + (.08 / 4)]^4
100000 [1 + (.08 / 4)]^4 ... total
subtract 100000 to find interest
To calculate the interest earned after a year with quarterly compounding, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Total amount including principal and interest
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
In this case, the principal amount (P) is $100,000, the annual interest rate (r) is 8% (or 0.08 in decimal form), the compounding periods per year (n) is 4 (quarterly), and the number of years (t) is 1.
Plugging these values into the formula, we get:
A = 100,000(1 + 0.08/4)^(4*1)
Simplifying further:
A = 100,000(1 + 0.02)^4
A = 100,000(1.02)^4
Using a calculator or spreadsheet, we can calculate (1.02)^4 to be approximately 1.0824.
A ≈ 100,000 * 1.0824
A ≈ $108,240
So, the total amount after a year, including the principal and interest, would be approximately $108,240. The interest earned would be the difference between this total amount and the principal:
Interest = $108,240 - $100,000
Interest ≈ $8,240
Therefore, the interest earned after a year with quarterly compounding would be approximately $8,240.