Question

11. When Tanya was born, her family put $2,500 into an account for her that earns

5.5% annually. Her family plans to use the money to purchase a trip for her when she
graduates from high school.
.
Package A
London
• Paris
$5,000
.
.
.
Package B
London
Paris
Madrid
$6,500
.
.
.
.
Package C
London
Paris
Madrid
Rome
$8,000
A. Write the formula to determine the amount of money in the account
after x years.

Answer 1

To determine the amount in Tanya's account after x years, use the compound interest formula A = P(1 + r/n)^(nt), with P=$2,500, r=5.5%, n=1, and t=x. After simplifying, the formula is A = $2,500(1 + 0.055)^x.

Step-by-step explanation:

To calculate how much money Tanya will have in her account after x years, we can use the formula for compound interest. The compound interest formula is:

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

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

In Tanya's case, the principal amount P is $2,500, the annual interest rate r is 5.5% or 0.055, and interest is compounded annually, so n is 1. Thus, after x years, the formula becomes:

A = $2,500(1 + 0.055/1)^(1*x) = $2,500(1 + 0.055)^x