223k views
5 votes
Emilio wants to invest $15,820 that he has just received as a prize from a contest. He researches certificates of deposit (CDs) at two different banks. Both CDs earn compound interest.

Bank West:

Annual Interest Rate: 3%
CD Length: 6 years
Frequency of Compounding: Quarterly
First Bank:

Annual Interest Rate: 4%
CD Length: 5 years
Frequency of Compounding: Monthly
a. How much money will Emilio have if he invests his money at Bank West?
b. How much money will Emilio have if he invests his money at First Bank?
c. How much more money will Emilio have if he invests at First Bank rather than at Bank West?

1 Answer

5 votes

Final answer:

Emilio will have $18,809.41 if he invests his money at Bank West, $19,875.45 if he invests his money at First Bank, and $1,066.04 more if he invests at First Bank rather than at Bank West.

Step-by-step explanation:

a. How much money will Emilio have if he invests his money at Bank West?

To calculate the future value of the investment, we can use the compound interest formula: A = P(1 + r/n)^(nt)

Where:

  • A is the future value of the investment
  • P is the principal amount (initial investment)
  • r is the annual interest rate in decimal form
  • n is the number of times interest is compounded per year
  • t is the number of years

Given that Emilio invests $15,820 at an annual interest rate of 3% for 6 years, with quarterly compounding, we can plug in the values into the formula:

A = 15820(1 + 0.03/4)^(4*6) = $18,809.41

Therefore, Emilio will have $18,809.41 if he invests his money at Bank West.

b. How much money will Emilio have if he invests his money at First Bank?

Using the same formula, but with an annual interest rate of 4%, a CD length of 5 years, and monthly compounding, we can calculate the future value:

A = 15820(1 + 0.04/12)^(12*5) = $19,875.45

Therefore, Emilio will have $19,875.45 if he invests his money at First Bank.

c. How much more money will Emilio have if he invests at First Bank rather than at Bank West?

The difference in their future values can be calculated by subtracting the amount from Bank West from the amount from First Bank:

19,875.45 - 18,809.41 = $1,066.04

Therefore, Emilio will have $1,066.04 more if he invests at First Bank rather than at Bank West.

User SleepyMurph
by
7.3k points