How much would you have to deposit today in order to have $5000 in 4 years in a bank account that pays 5% annual interest rate
5000=P*(1.05)^4
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5000/(1.05)^4
To calculate the deposit amount needed to have $5000 in 4 years with a 5% annual interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($5000)
P = the principal amount (deposit amount we want to find)
r = the annual interest rate (5% or 0.05)
n = the number of times interest is compounded per year (assume it's compounded annually, so n = 1)
t = the number of years (4 years)
Now let's substitute the given values into the formula:
$5000 = P(1 + 0.05/1)^(1*4)
Simplifying, we have:
$5000 = P(1 + 0.05)^4
Next, we'll isolate P by dividing both sides of the equation by (1 + 0.05)^4:
P = $5000 / (1 + 0.05)^4
Using a calculator, we can evaluate:
P ≈ $5000 / 1.2155
P ≈ $4115.73
Therefore, you would need to deposit approximately $4115.73 today in order to have $5000 in 4 years in a bank account that pays a 5% annual interest rate.
To calculate how much you would need to deposit in order to have $5000 in 4 years with a 5% annual interest rate, you can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, which is $5000 in this case
P = the principal amount, or the initial deposit
r = the annual interest rate, which is 5% in this case (in decimal form, so 0.05)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for, which is 4 years in this case
To solve for P, we rearrange the formula:
P = A / (1 + r/n)^(nt)
Substituting the given values:
P = 5000 / (1 + 0.05/1)^(1*4)
Simplifying the equation:
P = 5000 / (1.05)^4
Calculating:
P ≈ $4026.91
Therefore, you would need to deposit approximately $4026.91 today in order to have $5000 in 4 years in a bank account that pays a 5% annual interest rate.