Question

4-87 A 25-year-old engineer is opening an individual retirement account (IRA) at a bank. Her goal is to accumulate $1 million in the account by the time she retires from work in 40 years. The bank manager estimates she may expect to receive 6% nominal annual interest, compounded quarterly, throughout the 40 years. The engineer believes her income will increase at a 5% annual rate during her career. She wishes to start her IRA with as low a deposit as pos- sible and increase it at a 5% rate each year. Assuming end-of-year deposits, how much should she deposit the first year?

Answer 1

Future value of annuity=FV=$1000000

Rate of interest=r=6%/4=1.5% per quarter

Effective annual rate of interest per year=i=(1+r)^4-1=(1+1.5%)^4-1=6.1364%

Number of periods =n=40 years

Growth Rate of annual deposit=g=5%

We know that future value of growing (by fixed percentage) annuity is given by