Question

Emily wants to save for a down payment on a house. She plans to

save $500 per month for the next five years in a savings account
that earns an annual interest rate of 4%. What will be the future
value?

Answer 1

The future value of Emily's savings account will be $36,499.50.

Step-by-step explanation:

To find the future value of Emily's savings account, we can use the formula for compound interest.

The formula for compound interest is: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, Emily plans to save $500 per month for 5 years, so the principal amount is $500/month * 12 months/year * 5 years = $30,000. The annual interest rate is 4% or 0.04, and since the interest is compounded annually, n = 1. Finally, t = 5.

Plugging these values into the formula, we get:

A = $30,000(1 + 0.04/1)^(1*5) = $30,000(1 + 0.04)^5 = $30,000(1.04)^5 = $30,000(1.21665) = $36,499.50

Therefore, the future value of Emily's savings account will be $36,499.50.