Question

Vera wants to buy an antique car for $75,000 on her 36th birthday. She would like to begin with a yearly amount deposited in her money market account earning 6.5% on her 26th birthday, and increase the amount each year by the inflation rate of 4.5%. What amount should she plan on depositing on her 26th birthday?

$2,346

$3,521

$3,986

$5,456

Answer 1

Since first amount is deposited at her 26^th birthday and last amount at 36^th birthday, total time period for deposit is N = 11 years, and there is growth in amount equal to inflation rate of 4.5%, so present value of these amount is represents, following formula

Present value of geometric gradient = A1 x (1-(1+g)^n (1+i)^-n)/(i-g)

Here, I = 6.5% and g = 4.5%, and n = 11, A1 =?

And if we multiply this amount by compounding interest rate factor, it should exactly be equal to $75,000

So

A1 x (1+i)^n x (1-(1+g)^n (1+i)^-n)/(i-g) = $75,000

A1 x (1+.065)^11 x (1-(1+.045)^11 x (1+.065)^-11)/(.065-.045) = 75000

A1 x 1.999151 x 9.411452 = 75000

A1 = 3986.20 or $3,986 rounded ans is C