Question

Decide which of the two plans will provide a better yield. Plan A: $48,000 invested for 2 years at 1.5%, compounded quarterly Plan B: $48.000 invested for 2 years at 1.4%, compounded continuously Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A Plan B is better by $ (Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.) B. Plan A is better by $ (Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.) O C. Both plans are same.

Answer 1

We will calculate future values of both the plans as per below:

Plan A:

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $48000, r = rate of interest = 1.5% compounded quarterly. So, quarterly rate = 1.5% / 4 = 0.375%, n= time period = 2 * 4 = 8 quarters

now, putting theses values in the above equation, we get,

FV = $48000 * (1 + 0.375%)⁸

FV = $48000 * (1 + 0.00375)⁸

FV = $48000 * (1.00375)⁸

FV = $48000 * 1.03039671701

FV = $49459.04

So, plan A will give $49459.04

Plan B:

Here, we will use the following formula of continuous compounding:

FV = PV * e^(i*t)

where, FV is the future value , PV = Present value = $48000, i = rate of interest = 1.4%, t is the time period = 2 and e is the exponential factor whose value is 2.7183

Putting the values in the above formula, we get,

FV =$48000 * (2.7183)^{2 * 1.4%}

FV = $48000 * (2.7183)^0.028

FV = $48000 * 1.02839587691

FV = $49363

So, plan B will give $49363.

Option (B) is the correct answer

From the above we can see that Plan A is better by $96.04 (i.e. $49459.04 - $49363)