The Patel's wage replacement ratio is 70% of their pre-retirement income which is approximately $182,000 * 70% = $127,400. We need to adjust the pre-retirement income to today's dollars. Therefore, pre-retirement income in today's dollars = $123,689 ($127,400/ (1+0.03). They would like to retire at age 65 and are expecting monthly social security income of $4700 ($2100 for John and $2600 Asha) which they will receive at their FRA of 67. Because the Patel's are retiring 2 years earlier than FRA, their social security retirement income will be reduced by approximately 5/9 * 24 = 13.33%. Therefore, they will only receive $4,700 * (100% - 13.33%) = $4,073.50 which is approximately $4,073.50 * 12 = $48,882.00 per year. Therefore, their investments need to generate $123,689 - $48,882 = $74,807 per year. Their life-expectancy is 30 years in retirement.

Step 1 is to determine income for the 1^st year of retirement:

N = 25

I = 3%

PV = $74,807

PMT = 0

FV = $156,629.25.

Step 2 is to determine lump sum needed to fund all the remaining years of retirement. First calculate the real rate of return which is as follows:

Inflation (i) = 3% and Rate of return (Rn) = 5%. Real rate of return = [(1+Rn / 1+i) - 1] * 100. Real rate = [(1+5%)/ (1+3%) -1] * 100 = 1.94%. Set calculator in Begin mode:

N = 30

I = 1.94%

FV = 0

PMT = $156,629.25

PV = $3,605,673

Therefore, the Patel's require $3,605,673 at the start of their retirement to fully fund their post-retirement plans.