After how many years will a $2400 sapphire ring be worth at least $8000 if it increases in value by 10.5% p.a.

Question

I don't know the formula for this question and need help working it out and need help understanding the question.

Answer 1

At the end of each year the value of the ring will increase by 10.5%.

At the end of 1 year it will be worth 2400*(1.105).

At the end of n years it will be worth 2400*(1.105)ⁿ

You need to calculate n so that  2400*(1.105)ⁿ = 8000.

1.105ⁿ = 80/24 = 10/3.

n log 1.105 = log 10/3 which you can use a log table and/or your calculator to compute

n= 12.05

 

Answer 2

I assume that p.a. means "per annum"?

 

Let V(t) = value of the ring in t years

 

V(t) = 2400(1+0.105)^t

 

V(t) = 8000 when 2400(1.105)^t = 8000

 

                                   (1.105)^t = 3.33333

 

                            log(1.105)^t = log3.33333

 

                            tlog(1.105) = log3.33333

 

                                          t = log3.33333 / log1.105 ≈ 12.06 years