How much money would have to be deposited into a compound interest savings account earning 5% each year in order to accumulate $10,000 in 18 years?
To calculate the amount of money that needs to be deposited into a compound interest savings account to accumulate $10,000 in 18 years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($10,000 in this case)
P = the principal amount (the initial deposit we need to find)
r = the annual interest rate as a decimal (5% is 0.05)
n = the number of times interest is compounded per year (in this case, assumed to be compounded annually)
t = the number of years (18 years in this case)
Now, let's solve the equation:
$10,000 = P(1 + 0.05/1)^(1*18)
Simplifying further:
$10,000 = P(1.05)^18
To isolate P, divide both sides by (1.05)^18:
P = $10,000 ÷ (1.05)^18
Calculating this, the principal amount P will be approximately $4,452.89 (rounded to two decimal places).
Therefore, you would need to deposit around $4,452.89 into the compound interest savings account in order to accumulate $10,000 in 18 years at an interest rate of 5% per year.