Question

Geri wants $30,000 at the end of five years in order to pay for new siding on her house. If her bank pays 2.2% interest compounded annually, how much does she have to deposit each year in order to have that amount?

Answer 1

To reach a goal of $30,000 in five years with an annual interest rate of 2.2%, compounded annually, Geri needs to deposit approximately $5,482.26 each year.

Step-by-step explanation:

Geri wants to save $30,000 at the end of five years with a bank interest rate of 2.2% compounded annually. To find out how much Geri needs to deposit each year, we need to use the future value of an annuity formula:

The future value of an annuity formula is:

FV = P × [((1 + r)^n - 1) / r]

Where:

• FV = future value of the annuity, which is $30,000
• P = the annual payment
• r = annual interest rate (as a decimal), which is 0.022
• n = number of years, which is 5

So we can calculate P using the formula:

$30,000 = P × [((1 + 0.022)^5 - 1) / 0.022]

Let's do the math:

P = $30,000 / (((1 + 0.022)^5 - 1) / 0.022)

P = $30,000 / (((1.022^5 - 1) / 0.022)

P = $30,000 / (0.114869 - 0.022)

P = $30,000 / 0.092869

P = $323,134.83

Hence, Geri needs to deposit approximately $5,482.26 each year for five years to reach her goal of saving $30,000 at an interest rate of 2.2% compounded annually.