Question

James opens a savings account with principal y dollars that pays 1.82% interest compounded quarterly. Express his ending balance after one year algebraically.

a) y(1 + 0.0182/4)^4
b) y(1 + 0.0182)^4
c) y(1 + 0.0182/4)^1
d) y(1 + 0.0182)^1

Answer 1

The correct expression for James' ending balance after one year is y(1 + 0.0182/4)^4 (option a). The formula for compound interest is used to calculate the ending balance.

Step-by-step explanation:

The correct expression for James' ending balance after one year is y(1 + 0.0182/4)^4 (option a).

To calculate the ending balance, we use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the ending balance, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, P is y dollars, r is 0.0182 (1.82% as a decimal), n is 4 (compounded quarterly), and t is 1 (one year).

Substituting the values into the formula, we get A = y(1 + 0.0182/4)^4.