Compound Interest Calculation with Quarterly Compounding

What is the interest value if BD 13000 is invested on January 20, 2022, to October 12, 2022, at 6% interest and compounded quarterly?

Given that BD 13000 is invested on January 20, 2022, to October 12, 2022, at 6% interest and we need to find the interest value if it was compounded quarterly.

Interest Calculation:

The formula to calculate compound interest is given by: A = P[1 + (r/n)]^(nt)
Where,
P = Principal amount
r = annual interest rate
t = time in years
n = number of times interest applied per year
A = Amount after n years

Let the interest be compounded quarterly. Therefore, the interest rate per quarter would be: 6% / 4 = 1.5%
Time (t) = 8 months = 8/12 = 2/3 years
Number of times interest applied (n) = 4 (Quarterly)

Substituting the values in the above formula, we get:
A = 13000[1 + (1.5/100)]^(4/3 * 2)
A = 13000[1 + 0.015]^(8/3)
A = 13000[1.015]^2.667
A = 14223.14

Interest = A - P
Interest = 14223.14 - 13000
Interest = 1223.14

Therefore, the interest value if BD 13000 is invested on January 20, 2022, to October 12, 2022, at 6% interest and compounded quarterly is BD 1223.14.