Question

You have to wait for 3.5 years before starting to save for the purchase of a new car. You want to save towards the purchase of R12,500 car plus GST, Your savings rate is 5.2% compounded semi-annually and you want to be able to buy this car in 9 years. What is the size of your quarterly deposits?

Answer 1

$$FV=(1+i)P(\dfrac{(1+i)^n-1}{i})$$

$$P=FV\bigg(\dfrac{i}{(1+i)((1+i)^n-1)}\bigg)$$

$$P=12500\bigg(\dfrac{0.052/4}{(1+0.052/4)((1+0.052/4)^{(9-3.5)(4)}-1)}\bigg)$$

$$=488.11$$

Your quarterly deposit is R488.11.