Question

If a new college graduate wants a car costing $21,000, how much must be saved annually over the next four years if the funds earn 5%?

Answer 1

I'm assuming the funds earn 5% yearly?

Call x the amount he saves every year.  The first year's deposit will be multiplied by 1.05 three times, the next will be multiplied by 1.05 twice, the third will be multiplied by 1.05 once, and the fourth will not generate interest (as it will immediately be used to buy the car).

Therefore, x(1.05^3+1.05^2+1.05+1)=21000, so 4.31x=21000.  Dividing by 4.31, we see that x is approximately equal to 4872.