Question

Problem: Saving for Retirement 

Ann is now 25 years old and she is planning to start saving for retirement. She expects her income of $60,000 in the coming year to grow at the (nominal) rate of 5% a year until she retires at the age of 65. She wants to save a fixed percentage of her income per year. She wants to save enough money to be able to consume per year 50% of her income (in real terms) just before retirement (at age 65) for 20 years. Assume the inflation rate of 3%, and a nominal rate of return on Ann's savings of 6%. What fraction of income should Ann be saving?

Answer 1

Ann's current income = $60,000.00

Ann's income will increase by 5% each year.

Hence, Her income at the time of retirement = 60,000 * (1 + 0.05)⁴⁰ = 422399.32

Hence, her expenditure after retirement would be = 422399.32/2 = for 20 years

Now, Ann's saving will give her 6% return. Let total savings required for Ann at the time of retirement is x.

Hence, we have;

Now, let Ann saves y% of her income.

Hence, we have;

Hence,

Hence, y = 11.50%