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.
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?
1 answer
1 answer