Suppose $12,000.00 is invested in an account.Calculate the total interest earned by the end of 20 years if the interest is:(a) 6% simple interest: $(b) 6% compounded annually: $(c) 6% compounded quarterly: $(d) 6% compounded weekly: $(e) 6% compounded continuously: $

(a) Simple Interest: The formula for simple interest is I = PRT, where P is the principal amount, R is the rate of interest, and T is the time in years.

Here, P = $12,000, R = 6/100 = 0.06 (converting percentage to decimal), and T = 20 years.

So, I = 12000 * 0.06 * 20 = $14,400.00

(b) Compounded Annually: The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest. P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Here, P = $12,000, r = 0.06, n = 1 (since it's compounded annually), and t = 20 years.

So, A = 12000 * (1 + 0.06/1)^(1*20) = $38,430.73

The interest earned is A - P = $38,430.73 -$12,000 = $26,430.73

(c) Compounded Quarterly: Here, n = 4 (since it's compounded quarterly).

So, A = 12000 * (1 + 0.06/4)^(4*20) = $39,342.24

The interest earned is A - P = $39,342.24 -$12,000 = $27,342.24

(d) Compounded Weekly: Here, n = 52 (since it's compounded weekly).

So, A = 12000 * (1 + 0.06/52)^(52*20) = $39,557.48

The interest earned is A - P = $39,557.48 -$12,000 = $27,557.48

(e) Compounded Continuously: The formula for continuously compounded interest is A = Pe^(rt), where e is the base of the natural logarithm (approximately equal to 2.71828).

So, A = 12000 * e^(0.06*20) = $39,744.46

The interest earned is A - P = $39,744.46 -$12,000 = $27,744.46