If you received $100 for your birthday and put it in a bank with a 5% interest rate, you can calculate how much money you would have on your 65th birthday by using the concept of compound interest. Compound interest is the interest earned on both the initial amount of money deposited (the principal) and any interest that has already been earned.
To calculate the future value of your money, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (the initial $100)
r = the annual interest rate (5% or 0.05)
n = the number of times that interest is compounded per year (assuming it is compounded annually)
t = the number of years the money is invested for (65 - 17 = 48 years)
Plugging in the values into the formula, we get:
A = 100(1 + 0.05/1)^(1*48)
Simplifying the equation, we have:
A = 100(1.05)^48
Using a calculator, we can find that (1.05)^48 is approximately 12.578.
So, the future value of your investment would be:
A = 100 * 12.578
A = $1,257.80
Therefore, if you never touched the money and left it in the bank with a 5% interest rate, you would have approximately $1,257.80 on your 65th birthday.