A friend is celebrating her birthday and wants to start saving for her anticipated retirement.  She has the following years to retirement and retirement spending goals.            Years until retirement:     30 Amount to withdraw each year: $120,000 Years to withdraw in retirement: 25 Interest rate: 7.5%   Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires.  She wants to make equal annual deposits into her account for her retirement fund.

Maria, who is now 51 years old, is employed by a firm that guarantees her a pension of $35,000/year at age 65. What is the present value of her first year's pension if the inflation over the next 14 years is 3%/year compounded continuously? 4%/year compounded continuously? 6%/year compounded continuously? (Round your answers to the nearest cent.)

Suppose you start saving for retirement when you are 45 years old. You invest $5,000 the first year and increase this amount by 3% each year to match inflation for a total of 20 years. The interest rate is 10% per year. How much money will you have saved when you are 65 years old?

Suppose you think if you were to retire right now, you would have needed $50,000 each year to supplement your social security and maintain your desired lifestyle. But because there is on average 3% annual inflation, when you retire 30 years from now, you need more than $50,000 per year to maintain the lifestyle you like.    How much will be equivalent to $50,000 at retirement time when adjusted for inflation? What will be the face value of the bond that yields the equivalent of $50,000, found in #4 of Part B in coupon payment? How much annual payment in the retirement account is needed to accumulate the amount needed to purchase the bond when retiring?  What is the purchase power of the amount that will be received by your inheritors, measured in the current value of $ at the time of opening the retirement account?  (Hint: First calculate what the future value will be in 30 years, which is equivalent to $50,000 now and then solve the rest of the problem).