Question

Assume that you are 30 years old today, and that you are planning on retirement at age 65. You expect your salary to be 40,000$ one year from now and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this year's salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 10%.

The future value at retirement (65) of your savings is _____

Answer 1

Future value of growing annuity = First payment*[(1+r)^n – (1+g)^n]/(r-g)

Hence, value of savings at retirement = 40,000*8%*[{(1+10%)^35 - (1+5%)^35]/(10%-5%)]

= $1,445,530.97

Hence, the answer is $1,445,530.97