Question

(3) You desire to purchase a house in the future. You anticipate that you will need a $10,000 down payment. You estimate that you can save $150 per month from you salary, which will be deposited at the end of each month in a savings account paying 6% interest a year. (a) Will you have accumulated enough money at the end of four years for a down payment? (b) What if you deposited your money in a mutual fund account that earned 18% a year? (4) You would like to sell your house and are asking $180,000. A buyer makes an offer to purchase the house for $210,000, if he can pay the purchase price in installments for $70,000 per year for the next 3 years. Is this a good deal? What is the value of this $70,000 annuity to you today, assuming that you require a 12% rate of return?

Answer 1

3.

(a) Amount deposited each month = P = $150

Interest Rate = r = 0.06/12 monthly

Number of months = n = 4*12 = 48

Total Amount in account after 4 years = FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P
= P[(1+r)ⁿ -1]/r
= 150[(1+0.06/12)⁴⁸ -1]/(0.06/12)
= $8,114.67

We would not be able to save sufficient amount in 4 years

(b)

Interest Rate = r = 0.18/12 monthly

Total Amount in account after 4 years = FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P
= P[(1+r)ⁿ -1]/r
= 150[(1+0.18/12)⁴⁸ -1]/(0.18/12)
= $10,434.78

We would be able to save sufficient amount in 4 years

4.

Amount paid each year = P = $70000

Number of payments made = n = 3

Rate of Return = r = 12%

Present Value of payments made = PV = P + P/(1+r) + P/(1+r)²
= 70000 + 70000/(1+0.12) + 70000/(1+0.12)²
= $188,303.57

Hence, the value of the annuity today = $188,303.57

Hence, this is a good deal since the present value of the payments to be made in 3 years is greater than the current ask price of the house