(a) The formula for simple interest is I = Prt

I = 4000(0.05)(1) = 200

The account earned $200 in interest, so the new value is $4200.

(b) The formula for compound interest is A = P (1 + r⁄n) nt

The interest is compounded quarterly for a year, so n = 4 and t = 1.

A = 4000 (1 + 0.05⁄4) 4 = 4000(1.0125)4 ≈ 4000(1.05) = 4204

The new value is $4204, so the account earned $204 in interest.

(c) The formula for compound interest is A = P (1 + r⁄n) nt

The interest is compounded daily for a year, so n = 365 and t = 1.

A = 4000 (1 + 0.05⁄365) 365 = 4000(1.00014)365 ≈ 4000(1.0524) = 4210

The new value is $4210, so the account earned $210 in interest.

If this was a multiple-choice question, you could look at the answer choices to see how accurate the answer needed to be. Let’s say the answer options are:

(A) $200 (B) $210 (C) $4182 (D) $4200 (E) $4210

You could easily calculate that the value with simple interest would be $4200. Since you know that the amount with compound interest must be greater, the only possible answer choice is (E) and there is no need to do that calculation.