Question

A couple has $5,000 to invest and has to choose between three investment options.

Option A: 2 1/4% interest applied each quarter
Option B: 3% interest applied every 4 months
Option C: 4 1/2% interest applied twice each year
If they plan on no deposits and no withdrawals for 5 years, which option will give them the largest balance after 5 years? Use a mathematical model for each option to explain your choice.
a) Option A
b) Option B
c) Option C
d) Options A and B will yield the same balance after 5 years.

Answer 1

Option B will give the largest balance after 5 years, with a future value of $7,756.50.

Step-by-step explanation:

To determine which investment option will give the largest balance after 5 years, we need to calculate the future value of each option and compare the results. Let's calculate the future value for each option:

Option A:

Interest rate per quarter = 2.25% = 0.0225

Number of quarters in 5 years = 5 years * 4 quarters/year = 20 quarters

Future value = $5,000 * (1 + 0.0225)^20 = $5,000 * 1.5089 = $7,544.50

Option B:

Interest rate every 4 months = 3% = 0.03

Number of 4-month periods in 5 years = 5 years * 12 months/year / 4 months/period = 15 periods

Future value = $5,000 * (1 + 0.03)^15 = $5,000 * 1.5513 = $7,756.50

Option C:

Interest rate per semi-annual period = 4.5% = 0.045

Number of semi-annual periods in 5 years = 5 years * 2 periods/year = 10 periods

Future value = $5,000 * (1 + 0.045)^10 = $5,000 * 1.5250 = $7,625.00

Based on the calculations, Option B will give the largest balance after 5 years, with a future value of $7,756.50.