Question

Lydia has $2200

that she wants to invest in a CD account for 2.4
years, at which time she plans to close out the account and use the money as a down payment on a house. She finds one local bank offering an annual interest rate of 3.1%
compounded quarterly (Bank 1), and another bank offering an annual interest rate of 2.82%
compounded annually (Bank 2). Which bank should she choose?

Answer 1

To determine which bank Lydia should choose, we calculate the future value for both banks using the compound interest formula with the respective interest rates and compounding periods. Bank 1 offers an annual interest rate of 3.1% compounded quarterly, while Bank 2 offers 2.82% compounded annually. Lydia should compare the calculated future values and choose the bank with the higher amount.

Step-by-step explanation:

To determine which bank Lydia should choose for her CD account, we need to compare the final amount of money she would have after 2.4 years in each of the two banks, considering the different compounding periods and interest rates.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:

• A = the future value of the investment
• P = the principal amount ($2200)
• r = the annual interest rate (3.1%, or 0.031)
• n = the number of times interest is compounded per year (4 for quarterly)
• t = the time the money is invested (2.4 years)
  Plugging in the numbers from Bank 1:
  A = 2200(1 + 0.031/4)^(4*2.4)
  Calculate A to find the final amount from Bank 1.
  Using the same formula with Bank 2's interest rate (2.82%, or 0.0282) and annual compounding (n=1):
  A = 2200(1 + 0.0282/1)^(1*2.4)

Calculate A to find the final amount from Bank 2.
After calculating both A values, Lydia should compare them and choose the bank which offers the higher future value amount for her investment.