Caleb Brewster did an excellent job saving for retirement. He was able to save $

Question

Caleb Brewster did an excellent job saving for retirement. He was able to save $1,000,000 in an account that pays 12 percent per year. His plan was to eventually withdraw all his money by paying himself in equal installments every month during his 20 years of retirement, which he did for exactly 10 years. However, poor Mr. Brewster died exactly 10 years after he retired before receiving the remaining monthly payments he was due. How much money was left in Mr. Brewster's account on the day he died?

Explanation / Answer

Balance as on today = $1,000,000

Annual interest rate = 12%

Monthly interest rate = 12%/12 = 1%

No. of withdrawals = 20 years * 12 = 240

Equal monthly withdrawal = ($1,000,000 * 0.01) / ( 1 - 1.01-240) = $11,010.86

Balance left after 10 years = Present value of balance 120 installments

Present value of annuity = Annuity * {1-(1+r)-n}/r

Present value of remaining installments = $11,010.86 * (1-1.01-120)/0.01 = $767,462.70

Money left in Mr. Brewster's account on the day he died = $767,462.70

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