How much would you need to deposit in an account now in order to have $20,000 in
the account in 4 years? Assume the account earns 5% interest.
To determine how much you would need to deposit in an account now in order to have $20,000 in the account in 4 years, you can use the formula for compound interest. The formula is as follows:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, in this case $20,000
P = the principal amount (the initial deposit), which we want to find
r = the annual interest rate, which is 5% as given
n = the number of times that interest is compounded per year, let's assume it is compounded annually
t = the number of years the money is invested for, in this case 4
Now, we can substitute the given values into the formula and solve for P:
20000 = P(1 + 0.05/1)^(1*4)
Simplifying the equation, we get:
20000 = P(1.05)^4
Next, divide both sides of the equation by (1.05)^4 to isolate P:
P = 20000 / (1.05)^4
Using a calculator, we can calculate (1.05)^4 = 1.2155, so:
P = 20000 / 1.2155
P ≈ $16,446.27
Therefore, you would need to deposit approximately $16,446.27 in the account now in order to have $20,000 in the account in 4 years, assuming the account earns 5% interest compounded annually.
To calculate the amount you need to deposit in the account now, we can use the formula for the future value of a present amount with compound interest:
Future Value = Present Value * (1 + Interest Rate)^Time
Given that the future value is $20,000, the interest rate is 5%, and the time is 4 years, we can substitute these values into the formula:
$20,000 = Present Value * (1 + 0.05)^4
To solve for the present value (the amount you need to deposit now), we can rearrange the formula:
Present Value = Future Value / (1 + Interest Rate)^Time
Substituting the values:
Present Value = $20,000 / (1 + 0.05)^4
Now we can calculate it step by step:
Present Value = $20,000 / (1.05)^4
Present Value = $20,000 / 1.2155
Present Value ≈ $16,446.28
Therefore, you would need to deposit approximately $16,446.28 in the account now to have $20,000 in the account in 4 years.
x(1.05)^4 = 20000
solve for x