Final answer:
To determine how much money you need to deposit into an account earning Y percent on your 20th birthday in order to have X dollars, you can use the formula for compound interest: A = P(1 + r/n)^(nt). Let's substitute the values into the formula: X = P(1 + (Y/100)/1)^(1 * t). To solve for P (the principal amount), we can rearrange the formula: P = X / (1 + Y/100)^t. Therefore, the amount of money you need to deposit into the account is X / (1 + Y/100)^t.
Step-by-step explanation:
To determine how much money you need to deposit into an account earning Y percent on your 20th birthday in order to have X dollars, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value (X dollars)
- P is the principal amount (the amount you need to deposit)
- r is the annual interest rate (Y percent)
- n is the number of times interest is compounded per year (usually once for annual compounding)
- t is the number of years
Let's substitute the values into the formula:
X = P(1 + (Y/100)/1)^(1 * t)
X = P(1 + Y/100)^t
To solve for P (the principal amount), we can rearrange the formula:
P = X / (1 + Y/100)^t
Therefore, the amount of money you need to deposit into the account is X / (1 + Y/100)^t.