On the day of your birth and on every birthday since your grandparents placed $1,000 in a savings account that pays 5% compounded annually. Assuming zero withdrawals, how much was your account worth on your 18th birthday?"
1000 * 1.05^18
To calculate how much your account would be worth on your 18th birthday, we can use the formula for compound interest:
Future Value (FV) = P × (1 + r/n)^(n × t)
Where:
- P is the principal amount (initial deposit)
- r is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the principal amount (P) is $1,000, the interest rate (r) is 5% or 0.05, and the account compounds annually (n = 1). We need to calculate the future value (FV) when t = 18 years.
Using these values in the formula:
FV = $1,000 × (1 + 0.05/1)^(1 × 18)
= $1,000 × (1 + 0.05)^18
Now, let's calculate FV:
FV = $1,000 × (1.05)^18
Using a calculator, we find that (1.05)^18 ≈ 2.826 and rounding it to the nearest dollar:
FV = $1,000 × 2.826
≈ $2,826
Therefore, your savings account would be worth approximately $2,826 on your 18th birthday if your grandparents deposited $1,000 and it compounded annually at a 5% interest rate.