A couple is planning for retirement. Currently they have $75,000 saved. They would like to work 20 more years, and have enough saved to meet the following goals: pay themselves a retirement salary of $50,000 a year for a 30 year retirement (first payment in year 20, the same time period as their last savings installment); and buy a motor home that costs $90,000 today and is expected to increase in price 3% per year over the next 20 years. They use a long-term personal discount rate of 7% during both their work and retirement years. How much do they need to save in equal annual installments for the next 20 years to realize their goals? (First savings installment begins exactly one period from now, and the last savings installment occurs in exactly 20 years, which is also the time period when they would like to make the first withdrawal from their account and pay cash for the motor home.)
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