Question

Ms. Lan is considering purchasing a Sunrise apartment for $220,000. She will pay 10% down and $19,800 a year for 10 years. What is the real purchase price if Ms. Lan could get an interest rate of 5% on invested money (Don’t write currency symbol, round up to 2 decimal numbers

Answer 1

The amount of the down payment is $220,000 x 10/100 = $22,000.

The annual payment Ms. Lan will make for 10 years is $19,800, for a total of $19,800 x 10 = $198,000.

The total amount Ms. Lan will pay is $22,000 + $198,000 = $220,000.

To find the real purchase price, we need to find the present value of the $198,000 that Ms. Lan will pay over 10 years at an interest rate of 5%.

Using the present value formula, we get:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years.

Substituting the values we have, we get:

PV = $198,000 / (1 + 0.05)^10

PV = $198,000 / 1.6289

PV = $121,738.57

Therefore, the real purchase price is $22,000 + $121,738.57 = $143,738.45.

Answer 2

Step-by-step explanation:

The down payment is 10% of $220,000 = $22,000.

The total amount Ms. Lan will pay over 10 years is $19,800 x 10 = $198,000.

To find the real purchase price, we need to calculate the present value of the annual payments at an interest rate of 5%.

Using the formula for present value of an annuity:

PV = PMT x [(1 - (1 + r)^-n) / r]

where PMT is the payment, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $19,800, r = 5%/year = 0.05/year, and n = 10 years.

PV = $19,800 x [(1 - (1 + 0.05)^-10) / 0.05]

PV = $154,345.45

So the real purchase price of the apartment is the down payment plus the present value of the annual payments:

Real purchase price = $22,000 + $154,345.45

Real purchase price = $176,345.45 (rounded to 2 decimal places)