Use Figure 5.1. When their child was born, Elaine and Mike Porter deposited
$5,000 in a savings account at Tennessee Trust. The money earns interest at
6 percent compounded quarterly. How much will the account be worth when
their child celebrates her second birthday?
To calculate the amount in the account when their child celebrates her second birthday, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the account
P is the principal amount (the initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
Elaine and Mike Porter deposited $5,000 as the principal amount. The interest rate is 6 percent, which is 0.06 as a decimal. The interest is compounded quarterly, so n = 4. The time is from the birth of their child to her second birthday, which is 2 years.
Plugging the values into the formula:
A = 5000(1 + 0.06/4)^(4*2)
Simplifying the equation:
A = 5000(1 + 0.015)^8
A = 5000(1.015)^8
A = 5000(1.122
A ≈ $5610.92
Therefore, the account will be worth approximately $5610.92 when their child celebrates her second birthday.