Final answer:
To cover the current year's expense of $20,000, your parents would have needed to invest approximately $6,117.48 21 years ago in a bank account paying compound interest annually.
Step-by-step explanation:
To calculate how much your parents would need to invest 21 years ago to cover the current year's expense of $20,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount
- P is the principal amount (the initial investment)
- r is the annual interest rate (in decimal form)
- n is the number of times that interest is compounded per year
- t is the number of years
In this case, we want to find P, so we can rearrange the formula:
P = A / (1 + r/n)^(nt)
Plugging in the values:
P = 20000 / (1 + 0.07/1)^(1*21)
Calculating this expression gives:
P ≈ $6,117.48
Therefore, your parents would have needed to invest approximately $6,117.48 21 years ago in an account paying compound interest annually to cover the current year's expense of $20,000.