Question

Katie 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?

Answer 1

Katie should deposit $56,135.35 today to have $180,000 in 20 years at a 6% annual interest rate.

Step-by-step explanation:

To find out what Katie should deposit today in order to purchase a condo for $180,000 in 20 years with an annual interest rate of 6%, we can use the formula for the present value (PV) of a lump sum:
`PV = FV / (1 + r)^n`, where FV is the future value, r is the annual interest rate (expressed as a decimal), and n is the number of periods (years).

First, we convert the annual interest rate from a percentage to a decimal form: 6% = 0.06.

Next, we plug in the values into the formula:

PV =
`$180,000 / (1 + 0.06)^20`

Now we calculate the denominator
`(1 + 0.06)^20:`

`(1 + 0.06)^20 ≈ 3.20713547289`

Then, we can find the PV:

PV = $180,000 / 3.20713547289 = $56,135.35 (approximately)

Therefore, Katie should deposit $56,135.35 today to have $180,000 in 20 years, assuming a 6% annual return.