Assume that you are $30$ years old today, and that you are

planning on retirement at age $65.$ Your current salary is $$45,000$

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 $31$st 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 $7\%,$ what is the present value of your retirement

savings?