Question

There are two investment plans to be chosen by investing $5500 for 5 years: (a) Plan A paying 13.5% compounded quarterly. (b) Plan B paying a lump sum of $10,500 when due. Which is the better choice?

a) Plan A
b) Plan B

Answer 1

After calculating the future value of Plan A, which yields approximately $11,343.86 due to compound interest, it is evident that Plan A is a better option than Plan B, which offers a lump sum of $10,500.

Step-by-step explanation:

The question involves comparing two investment plans to determine which one is a better choice after 5 years. Plan A offers a 13.5% annual interest rate compounded quarterly, while Plan B offers a lump sum payment of $10,500 at the end of the period.

First, we will calculate the future value of Plan A using the compound interest formula: FV = P (1 + r/n)^(nt), where P is the principal amount ($5500), r is the annual interest rate (13.5% or 0.135), n is the number of times the interest is compounded per year (4 for quarterly), and t is the number of years (5).

Substituting the given values into the formula:

FV = 5500 (1 + 0.135/4)^(4*5) = 5500 (1 + 0.03375)^(20) = 5500 * (1.03375)^(20) = $11,343.86 approximately.

Since the future value of Plan A is $11,343.86, and Plan B offers a lump sum of $10,500, Plan A provides a higher return after 5 years and is therefore the better choice.