Peter deposit k180,600.00 with BSP which offers 6 1/4% per annum interest. Calculate the interest earned after 6 years if it is compounded:

180,600.00 (1+.0625)^6

K3750

To calculate the interest earned after 6 years with compound interest, we'll use the formula:

A = P(1 + r/n)^(nt)

Where:
A = the final amount (including principal and interest)
P = the principal amount (the initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years

In this case:
P = k180,600.00
r = 6 1/4% per annum, which can be written as 6.25% or 0.0625 in decimal form
n = 1 (interest compounded annually)
t = 6 (6 years)

So, plugging the values into the formula:

A = k180,600.00(1 + 0.0625/1)^(1*6)

We can solve this equation step by step.

First, calculate the interest rate per compounding period:

0.0625/1 = 0.0625

Next, add 1 to the interest rate per compounding period:

1 + 0.0625 = 1.0625

Then raise this sum to the power of the number of compounding periods:

1.0625^6 = 1.4084

Finally, multiply the result by the principal amount:

k180,600.00 * 1.4084 = k254,288.34

Therefore, the interest earned after 6 years, compounded annually, would be approximately k73,688.34 (k254,288.34 - k180,600.00).