Final answer:
After depositing $100 into a bank account with an annual compound interest rate of 5% at age 17, by age 65, you would have approximately $$1040.1, having used the formula A = P(1 + r/n)^(nt) to calculate compound interest over 48 years.
Step-by-step explanation:
To calculate how much money you would have on your 65th birthday after depositing $100 on your 17th birthday with an annual compound interest rate of 5%, you can use the formula for compound interest:
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.
If the interest is compounded annually (n=1), we plug in the values:
- P = $100
- r = 5% or 0.05
- n = 1
- t = 65 - 17 = 48 years
The formula becomes:
A = 100(1 + 0.05/1)^(1*48)
Calculating this
A = 100(1 + 0.05)^48
A = 100(1.05)^48
A ≈ 100(10.401)
A ≈$1040.
By your 65th birthday, you would have approximately $1040.1