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.
Is it compounded Daily, Monthly, or
Annualy? Since the compounding frequency is not given, I'll assume
simple Interest:
P = Po + I.
P = Po + Po*r*t = $20,000.
Po + Po*0.05*4 = 20,000
Po + 0.2Po = 20000
1.2Po = 20000
Po = $16,666.67 = Initial deposit.
Well, if you want to have $20,000 in the account in 4 years, and assuming the account earns 5% interest, I would say you should deposit...your hopes and dreams! Because let's be honest, with that interest rate, you'll need a lot more than just money to reach that goal! But hey, at least you'll have a good laugh along the way!
To calculate the amount you would need to deposit in an account now to have $20,000 in the account in 4 years, you can use the formula for compound interest:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment ($20,000)
P = the principal amount (the amount you need to deposit now)
r = the annual interest rate (5% or 0.05)
n = the number of times that interest is compounded per year (assumed to be once a year)
t = the number of years (4 years)
Plugging in these values, we have:
20,000 = P (1 + 0.05/1)^(1*4)
Simplifying:
20,000 = P (1.05)^4
Dividing both sides by (1.05)^4:
P = 20,000 / (1.05)^4
Using a calculator:
P ≈ $17,308.97
Therefore, you would need to deposit approximately $17,308.97 into the account now in order to have $20,000 in the account in 4 years.
To calculate the amount you need to deposit in an account to have $20,000 in 4 years with a 5% interest rate, you can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future amount (in this case, $20,000)
P = the principal amount (the amount you need to deposit)
r = the annual interest rate (5% or 0.05)
n = the number of times interest is compounded per year (assuming it's compounded annually, n = 1)
t = the number of years (4)
Now, let's substitute the values into the formula:
20000 = P(1 + 0.05/1)^(1*4)
Simplifying the equation:
20000 = P(1.05)^4
We can now isolate P by dividing both sides of the equation by (1.05)^4:
P = 20000 / (1.05)^4
Using a calculator, evaluate (1.05)^4, which equals approximately 1.21550625:
P ≈ 20000 / 1.21550625
P ≈ 16435.37
Therefore, you will need to deposit approximately $16,435.37 in the account now to have $20,000 after 4 years with a 5% interest rate.