6 years ago, Luther won some money in the lottery and put it in a bank account that earns 8% interest compounded monthly. If Luther currently has $6,000.00 in the bank account, how much interest has he earned?

Answer: the interest earned is $643

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

A = $6000

r = 8% = 8/100 = 0.08

n = 12 because it was compounded 12 times in a year.

t = 6 years

Therefore,.

6000 = P (1 + 0.08/12) ^6 * 12

6000 = P (1.0067) ^72

6000 = 1.12P

P = 6000/1.12

P = 5357

The interest earned is

6000 - 5357 = $643

2281.38

Step-by-step explanation:

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

6000=P (1+0.08/12) ^12*6

P=6000 / (1+0.08/12) ^72

P=3718.62

This P value is the money he started with.

6000-3718.62=2281.38

Luther earned 2281 dollars over 6 years.