Final answer:
To have a balance of $26,831.17 in five years in an account with 6.4% interest compounded monthly, the amount to be deposited today is $19,904.69 after performing the compound interest calculation and rounding to two decimal places.
Step-by-step explanation:
To determine how much should be deposited in an account with 6.4% interest compounded monthly to have a balance of $26,831.17 five years from now, we use the formula for compound interest:
P = A / (1 + r/n)^(nt)
- P = principal amount (the initial amount of money)
- A = the future value of the investment/loan, including interest
- r = annual interest rate (decimal)
- n = number of times that interest is compounded per year
- t = number of years the money is invested or borrowed for
In this case, we have A = $26,831.17, r = 0.064, n = 12 (monthly compounding), and t = 5 years.
Plugging in the values:
P = $26,831.17 / (1 + 0.064/12)^(12*5)
P = $26,831.17 / (1 + 0.0053333)^(60)
P = $26,831.17 / 1.348856
P = $19,904.69
The amount that needs to be deposited today is $19,904.69 when rounded to two decimal places.