Question

You have $300 you want to set aside in a savings account. There are 2 banks you are considering - ABC, which offers a monthly compound and WXY, which compounds continuously. They both offer a 1.59% interest rate. Find the difference in the interest earned after 5 years.

A) $12.88

B) $14.15

C) $14.54

D) $12.46

Answer 1

To find the difference in interest earned after 5 years between two banks with the same interest rate but different compounding methods (monthly for ABC and continuously for WXY), we apply the monthly compounding formula and continuous compounding formula to the principal amount of $300 at 1.59% interest.

Step-by-step explanation:

Calculating the Difference in Interest

To find the difference in the interest earned after 5 years in two banks offering different compounding methods but the same interest rate of 1.59%, we need to use the formulas for monthly compounding and continuous compounding respectively.

For ABC Bank with monthly compounding:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money accumulated after n years, including interest.

P = the principal amount ($300)

r = the annual interest rate (decimal) (0.0159)

n = the number of times that interest is compounded per year (12)

t = the time the money is invested for (5 years)

For WXY Bank with continuous compounding:

A = Pe^(rt)

Where:

e is the base of the natural logarithm, approximately equal to 2.71828

P, r, and t are defined as above

Using these formulas, we calculate the difference in interest earned and determine which answer choice is correct.