Katie Hector wants to purchase a condo in Oxford, MS, in 20 years. The cost of the condo is expected to be $180,000. Assuming she can earn 6% annually, what should Katie deposit today?
$126,900
56124
P*1.06^20 = 180000
P = 56125
with a deposit of 126900, she only needs 1.76% interest. How did you arrive at that figure?
To calculate the deposit Katie should make today, we need to use the present value formula, considering the cost of the condo in 20 years and the annual interest rate.
The formula for calculating the present value (PV) is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest rate
n = Number of years
In this case:
FV = $180,000
r = 0.06 (6% expressed as a decimal)
n = 20 years
Substituting these values into the formula:
PV = $180,000 / (1 + 0.06)^20
PV = $180,000 / (1.06)^20
PV = $180,000 / (1.425761357)
PV ≈ $126,221.97
Therefore, Katie should deposit approximately $126,221.97 today to purchase the condo in 20 years.
To determine the amount Katie should deposit today, we can use the concept of present value. Present value is the current worth of a future amount of money, adjusted for interest earned or inflation over time.
Here's how to calculate the present value:
1. Identify the future value: In this case, the future value is $180,000, which is the cost of the condo in 20 years.
2. Determine the interest rate: The interest rate provided is 6% annually. This is the rate at which Katie's deposit will grow over the 20-year period.
3. Calculate the present value using the formula: Present Value = Future Value / (1 + Interest Rate)^n
Where:
- Future Value is $180,000
- Interest Rate is 6% or 0.06
- n is the number of years, which is 20.
Plugging these values into the formula, we get:
Present Value = $180,000 / (1 + 0.06)^20
4. Calculate the present value:
Present Value = $180,000 / (1.06)^20
Present Value = $126,899.87 (rounded to $126,900)
Therefore, Katie should deposit $126,900 today to have enough to purchase the condo in 20 years, assuming a 6% annual interest rate.