To calculate the amount Taylor had in her account on her 17th birthday, we need to calculate the future value of the monthly deposits over 17 years.
a. To calculate the future value, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $60 (monthly deposit)
r = 2.40% = 0.024 (annual interest rate)
n = 12 (compounded monthly)
t = 17 (number of years)
Substituting these values into the formula, we can calculate the future value:
A = 60(1 + 0.024/12)^(12*17)
A ≈ $14,085.55 (rounded to the nearest cent)
Therefore, Taylor had approximately $14,085.55 in her account on her 17th birthday.
b. To calculate her mother's total investment, we multiply the monthly deposit by the number of months (17 years * 12 months per year):
Total investment = $60 * (17 * 12)
Total investment = $12,240
Her mother's total investment is $12,240.
c. To calculate the interest earned, we subtract the total investment from the future value:
Interest = Future value - Total investment
Interest = $14,085.55 - $12,240
Interest ≈ $1,845.55 (rounded to the nearest cent)
The investment earned approximately $1,845.55 in interest.