Question

Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $35,000 and you expect your salary to increase at a rate of 4% per year as long as you work. To save for 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 retirement. Assume that your discount rate is 9%. If you stick to this plan, the present value (at age 30) of your retirement savings is ____. How much do you expect to have when you retire?

Answer 1

Answer:

* The present value (at age 30) of retirement savings is $46,982.

* Amount expect when retiring: $959,089.

Explanation:

* The present value (at age 30) of retirement savings:

The contribution that is made on the 31st birthday = 31 years old salary * 8% = 30 years old salary * 1.04 * 8% = 35,000 * 1.04 * 8% = $2,912.

We apply the formula for calculating the present value of growing annuity to determine the present value of retirement savings at age 30:

[2,912 / ( 9% - 4%)] * [ 1 - [(1+4%)/(1+9%)]^35 ] = $46,982.

* Amount expect when retiring:

We apply the formula for calculating the future value of growing annuity to determine the future value of retirement savings at age 65:

[2,912/ (9% - 4%) ] * [ 1.09^35 - 1.04^35 ] = $959,089