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# Answer to Question #138154 in Finance for CH Tan

Question #138154
A man is planning to retire in 25 years. He wishes to deposit a regular amount every three
months until he retires, so that, beginning of one year following his retirement, he will
receive annual payments of $60,000 for the next 10 years. How much must he deposit if the interest rate is 6 percent compounded quarterly? 1 Expert's answer 2020-10-23T07:20:26-0400 solution Present value of benefits at retirement "Duration\\ n=10\\ years" "Payments\\ p= 60,000" "Interest\\ r=0.06" Compounding is done quarterly. Therefore, the effective annual rate is "i= (1+\\frac{0.06 }{4 })^4-1=0.061364" "A= p * \\frac{1-(1+i)^{{-n}} }{i}" "= 60,000 * \\frac{1-(1.061364)^{-10} }{0.061364}= \n438,766.34272" The deposits to be accumulated quarterly (every three months) should equal 438766.34272 "A = c \\ * \\frac{(1+\\frac{r}{4})^{t*4}-1}{\\frac{r}{4} }" "438,766.34272 = c \\ * \\frac{(1+\\frac{0.06}{4})^{25*4}-1}{\\frac{0.06}{4} }" "438,766.34273= 228.803*c" "C= 1,917.6596" Answer. He must deposit$ 1,917.6596

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