Final answer:
Jane will calculate the future value of her $12,500 deposit using the compound interest formula with a 7% biannual rate over 15 years, which is applied to determine how much she will have at the end of the period.
Step-by-step explanation:
Calculating Compound Interest Over 15 Years
Jane deposited $12,500 into a bank account with a biannual interest rate of 7%. To calculate the total amount she will have in 15 years, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($12,500)
r = the annual interest rate (decimally)
n = the number of times that interest is compounded per year (2 for biannual)
t = the time the money is invested or borrowed for, in years (15).
First, we convert the annual interest rate from a percentage to a decimal by dividing by 100:
7% / 100 = 0.07. Then, we apply the formula:
A = $12,500 * (1 + 0.07 / 2) ^ (2 * 15)
A = $12,500 * (1 + 0.035) ^ (30)
A = $12,500 * (1.035)^30
Computing this gives us the total amount in Jane's account after 15 years.