Question

Finnick has just been offered a job earning $75,000 a year. Finnick is paid once per year with his first check received one year from today. He anticipates his salary to grow by 2% per year until his retirement in 40 years. Assuming an interest rate of 10%, calculate the present value of his lifetime salary.

Answer 1

Here we will use the following formula for present value of annuity with growth rate.

Present value = P / r-g (1- (1+g / 1+r)ⁿ)

where, P= First payment, r= rate of interest, g= growth rate, n= no. of periods.

P= $75000, r = 10%, g= 2%, n= 40

Now putting these values into this equation, we get,

Present value = $75000 / 10% - 2% (1- (1+2% / 1+10%)⁴⁰)

Present value = $75000 / 8% (1- (1+.02 / 1+.10)⁴⁰)

Present value = $75000 /.08 (1- (1.02 / 1.10)⁴⁰)

Present value = $937500 (1- (0.927272)⁴⁰)

Present value = $937500 (1- 0.487864772)

Present value = $937500 (0.512135228)

Present value = $480126.77625