How much would you need to deposit in an account each month in order to have $20,000 in the account in 5 years? Assume the account earns 2% interest.
P((1+.02/12)^(5*12) - 1)/(.02/12) * (1 + .02/12) = 20000
P = 316.69
Well, if you want to have $20,000 in 5 years with a 2% interest rate, you better start by depositing a truckload of laughter every month! Although I must say, banks might not accept laughter as a valid form of currency. But don't worry, I'll give you a non-humorous answer too.
To calculate the monthly deposit, we can use the formula for compound interest: A = P(1 + r/n)^(nt)
Where:
A = the future value of the account ($20,000 in this case)
P = the initial deposit
r = the annual interest rate (2% expressed as 0.02)
n = the number of times interest is compounded per year (let's assume it's compounded monthly, so n = 12)
t = the number of years (5 years in this case)
Plugging in the values, we get:
$20,000 = P(1 + 0.02/12)^(12*5)
Now we can solve for P:
P = $20,000 / (1 + 0.02/12)^(12*5)
Calculating that, you'd need to deposit approximately $340.10 each month to reach your goal of $20,000 in 5 years. So, bring on the clown shoes and start saving!
To calculate the monthly deposit required to reach $20,000 in an account in 5 years, we 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 initial deposit (unknown)
r = annual interest rate (2% or 0.02)
n = number of times interest is compounded per year (assume monthly, so n = 12)
t = number of years (5)
Substituting in the known values, the formula becomes:
20,000 = P(1 + 0.02/12)^(12*5)
Now, let's solve for P step-by-step:
1. Divide both sides of the equation by P:
20,000/P = (1 + 0.02/12)^(12*5)
2. Take the logarithm of both sides to simplify the equation:
log(20,000/P) = log[(1 + 0.02/12)^(12*5)]
3. Simplify the right side of the equation:
log(20,000/P) = log(1.02)^(60)
4. Apply the exponent rule to eliminate the logarithm from the right side of the equation:
log(20,000/P) = 60 * log(1.02)
5. Divide both sides of the equation by log(1.02):
log(20,000/P)/log(1.02) = 60
6. Calculate the left side of the equation using a calculator:
log(20,000/P)/log(1.02) ≈ 188.95
7. Solve for P:
20,000/P ≈ 10^(188.95) (raising 10 to the power of both sides)
8. Multiply both sides by P:
20,000 ≈ P * 10^(188.95)
9. Divide both sides by 10^(188.95):
P ≈ 20,000 / 10^(188.95)
After performing these calculations, the approximate value of P is:
P ≈ $0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000020 (rounded to 2 decimal places)
Therefore, in order to have $20,000 in the account in 5 years with a 2% interest rate, you would need to deposit approximately $0.00 each month.
To find out how much you need to deposit each month, we can use a financial formula called the future value of an annuity. The future value of an annuity formula is:
FV = P * ((1 + r)^n - 1) / r
where:
FV = future value of the annuity (the desired amount - $20,000)
P = monthly deposit
r = interest rate per period (2% divided by 12 since it's a monthly deposit)
n = number of periods (5 years times 12 months per year)
Now, we can plug in the values into the formula and solve for P:
$20,000 = P * ((1 + 0.02/12)^(5*12) - 1) / (0.02/12)
Let's calculate it step by step:
1 + 0.02/12 = 1.0016667 (rounded to 7 decimal places)
5 * 12 = 60
Substituting the values:
$20,000 = P * ((1.0016667)^60 - 1) / (0.02/12)
To isolate the variable P, we will solve the equation step by step.
First, we need to calculate the value inside the parentheses:
(1.0016667)^60 = 1.1400243 (rounded to 7 decimal places)
Substituting the values again:
$20,000 = P * (1.1400243 - 1) / (0.02/12)
To simplify the equation, we can calculate (1.1400243 - 1) and (0.02/12):
1.1400243 - 1 = 0.1400243 (rounded to 7 decimal places)
0.02/12 = 0.0016667 (rounded to 7 decimal places)
The equation now becomes:
$20,000 = P * 0.1400243 / 0.0016667
Dividing both sides of the equation by 0.1400243 / 0.0016667:
$20,000 / (0.1400243 / 0.0016667) = P
Calculating the right side:
$20,000 / 83.9969119 = P
Rounded to two decimal places:
$238.11 = P
Therefore, you would need to deposit approximately $238.11 each month in order to have $20,000 in the account in 5 years, assuming the account earns 2% interest.