Have $800,000 for retirement in 20years account earns 8% interest. How much do you need to deposit each month?
the bot is making so many mistakes in arithmetic on calculators
I get $1358.19
I apologize for the error in my previous response. You are correct, the monthly deposit needed to reach $800,000 in 20 years with an 8% interest rate is $1,358.19, not $1,557.08. Thank you for bringing it to my attention.
To calculate how much you need to deposit each month for retirement, you can use the formula for future value of an ordinary annuity:
FV = P * [(1 + r)^(n - 1)] / r
Where:
FV = Future Value (in this case, $800,000)
P = Monthly deposit
r = Monthly interest rate (8% divided by 12 months, which is 0.08/12)
n = Number of months (20 years multiplied by 12 months, which is 20 * 12)
Plugging in the values:
$800,000 = P * [(1 + (0.08/12))^(20*12 - 1)] / (0.08/12)
To solve for P, we need to isolate it on one side of the equation. Multiply both sides by [(0.08/12)] and divide by [(1 + (0.08/12))^(20*12 - 1)]:
P = ($800,000 * (0.08/12)) / [(1 + (0.08/12))^(20*12 - 1)]
Calculating this equation will give you the monthly deposit amount you need for your retirement account.
To calculate the monthly deposit needed to reach $800,000 in 20 years with an 8% interest rate, we can use the formula for the future value of an annuity:
FV = Pmt x [(1+i)^n - 1]/i
where:
FV = future value (desired amount of $800,000)
Pmt = monthly deposit
i = interest rate per month (8%/12 = 0.0066667)
n = number of months (20 x 12 = 240)
Plugging in the values, we get:
800,000 = Pmt x [(1+0.0066667)^240 - 1]/0.0066667
Simplifying the equation, we get:
Pmt = 800,000 / [(1+0.0066667)^240 - 1]/0.0066667
Pmt = $1,557.08
Therefore, a monthly deposit of $1,557.08 is needed to reach $800,000 in 20 years with an 8% interest rate.