Question

You can earn 6% p.a. interest on your money (compounded monthly). You wish to purchase a house in exactly 5 years, which you expect would then cost $240,000. You need to save up 50% of this amount as you can borrow the rest. What monthly amount would need to be saved to enable you to achieve your objective? Your first monthly deposit will be made one month from now, and your last deposit will be made on the day you purchase the house.

Answer 1

• Here, Interest rate is given 6% p.a. which is compounded monthly. Thus we have to consider monthly interest rate i.e. 0.5%
• we have to purchase a house after 5 years, so the period (n) = 5. However we have to make monthly deposits. Hence, we shall consider the period (n) = 5*12 = 60.
• Cost of the house would be $240,000 after 5 years, out of which 50% i.e. $120,000 we have to save over this period. Hence, Future Value(FV) of Annuity = $120,000.

Amount of monthly deposits to be made is calculated using formula of FV of Annuity as explained in the image attached here :-