Could you guys help me out with a growing annuity question?

Question

Mary is now 40 years of age and makes $40,000 a year. She expects her income to increase 2% over inflation. She wants to accumulate $500,000 in real terms to retire at age 70.

What fraction of her income does she need to set aside? Assume her retirement funds expected real return of 5% p.a. Ignore taxes.

Thanks so much, I was trying the question and got stuck :/

Answer 1

On the average, she needs to set aside 12.74% of her income.

$40,000 with 2% annual growth will grow to $72,500 in 30 years.  So, $56,250 is the average, annually. then $7,168 annually / $56,250 = 12.74% she needs to set aside.

Answer 2

She has to set aside $7,167pa,

which is 17.9% of her income.

.