Final answer:
To find out how much Omar must deposit now to have $80,000 in 20 years in an account with a 1.75% interest rate compounded monthly, we use the compound interest formula. By plugging in the values, we establish the initial deposit required to reach his goal.
Step-by-step explanation:
Omar wants to ensure that he has $80,000 in an account after 20 years by investing a certain amount now in an account that yields 1.75% interest, compounded monthly. To find out how much he needs to deposit now, we can use the formula for compound interest:
P = A / (1 + r/n)nt
Where:
- P is the principal amount (the initial amount of money)
- A is the future value of the investment/loan, including interest
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per year
- t is the number of years the money is invested or borrowed for
In this case:
- A = $80,000
- r = 0.0175 (1.75% expressed as a decimal)
- n = 12 (compounded monthly)
- t = 20 (years)
Now we can plug in these values to find P:
P = $80,000 / (1 + 0.0175/12)12*20
After calculating the denominator and then dividing $80,000 by that number, we get the amount Omar needs to deposit today, which completes our step-by-step explanation.