Question

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 (a) (b) (c) (a) (b) (c) (a) (b) (a) (b) (c) (a) (b) (c) 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 possible and increase it at a 5% rate each year. Assuming end-of-year deposits, how much should she deposit the first year

Answer 1

Answer:

The minimum deposit will be of 3,081 and after 40 year it will get 1,000,000 dollars

Explanation:

We have to solve for the C of an annuity growing

$\frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}$

g 0.05

r 0.06

C 3,081

n 40

$C \frac{1-(1+0.05)^{40}\times (1+0.06)^{40} }{0.06-0.05} = 1,000,000$

$C \times 324.57 = 1,000,000$

$C = 1,000,000/ 324.57 = 3,081$